May 9, 2022
Simple interest is interest calculated on the principal portion of a loan or the original contribution to a saving account. Simple interest does not compound, meaning that an account holder will only gain interest on the principal, and a borrower will never have to pay interest on interest already accrued.
It is a sum which is paid by the borrower to the lender for using the money for a specific period of time. The money borrowed is the principal.
The rate at which the interest is calculated on the principal is called the rate of interest. The time for which the money is borrowed is the time and the total sum of principal and interest is called amount.
Simple Interest is the interest calculated on the original principal at any rate of interest for any period of time, then it is called simple interest.
If P = Principal,
R = Rate percent per annum,
T = Number of years,
SI = Simple Interest and
A = Amount
Then,
73 days = ⅕ yr
146 days = ⅖ yr
219 days = ⅗ yr
292 days = ⅘ yr
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The formula of simple interest is:
Simple Interest = Principal x Time Period x Rate of Interest / 100
Principal = 100 x Simple Interest / Rate of Interest x Time period
Rate of Interest = 100 x Simple Interest / Principal x Time Period
Time = 100 x Simple Interest / Principal x Rate of Interest
Amount = Principal x Simple Interest
Here, the interest is calculated on the original principal, i.e., the principal, to calculate the interest it remains constant throughout the time period. The interest earned on the principal is not taken into account for the purpose of calculating interest for later years.
In this article, you will get to know how to solve simple interest problems for NID.
The key to success in the exam is planning a well-structured study plan for NID and executing it effectively.
Before solving the simple interest problems for NID we should know all the parameters which will help in solving simple interest problems.
The fractional value of 25% is ¼, the fractional value of 20% is ⅕, and the fractional value of 33.33% is ⅓.
For example: In a question the rate of interest is given as 8.33% per annum so it will be 1/12 in the fractional form. Here that 1/12 means that 12 the denominator is the principal amount and 1 the numerator is the interest when you have received or paid on the principal amount in one year.
To help you get an idea about the type of questions asked in the exam, we have curated few sample questions from the previous year's NID Question papers.
Let us understand with an example:
For example 1: Sagar borrows Rs. 50,000 from a bank for 5 years. What is the rate of simple interest charged by the bank if after 5 years Sagar had to pay Rs. 66,000 to the bank?
Answer: 6.4 %
Solution:
This question can be solved in a fraction of seconds by using the simple interest formula but we will solve it by a different method so that you can easily understand the simple interest concept.
Once you have understood the simple interest concept you can easily solve any kind of question related to simple interest in seconds.
To given: sagar has borrowed rs. 50,000 from a bank for 5 years
And, after 5 years, Sagar will pay rs. 66,000 to the bank.
To find: the rate of interest on which sagar had borrowed the money from bank
Let us find out,
Sagar had borrowed Rs. 50,000 and he has to pay Rs. 66,000 after 5 years
Read more: Previous year exam analysis for NID entrance exam
So,
In this case we can say that the additional amount which sagar is paying is our simple interest
So, we will see the additional amount by subtracting Rs. 50,000 from Rs. 66,000.
The additional amount which he will pay as a simple interest will be 66,000 - 50,000 = 16,000.
So, the simple interest for 5 years will be Rs. 16,000
Now, we have to find at what rate of interest per annum he is paying the interest to the bank
So, the total simple interest for 5 years is Rs. 16,000
So the simple interest for 1 year will be 16000/5 = 3,200
Rate of interest = simple interest is what percentage of principal per year
Now, see below
Simple interest = Rs. 3,200 for 1 year
Principal amount = Rs. 50,000
Rate of interest = simple interest of 1 year / principal amount * 100
Rate of interest = 3200 / 50000 x 100
Rate of interest = 6.4 %
Read more: Important questions with answers for the NID CAT exam
So, the rate of interest on which sagar will pay the interest to the bank every year will be 6.4%
Let us understand the concept more by solving one more example
For Example 2:
After how many years would an amount double itself at 15% rate of simple interest?
Answer: in 7 years approximately the invested amount will be doubled.
Explanation:
To given: rate of simple interest 15%
To find: In what time the principal amount will be doubled..
Solution:
First we will convert percentage into fraction
So,
5% = 1/20
10% = 1/10
15% = 3/20
When you have converted percentage into fraction
It means
That 15% = 3 / 20
As we have mentioned above, if the rate of interest is given in percentage and we have converted that into a fraction then the numerator will be assumed as the interest amount and the denominator will be assumed as the principal amount.
So, in this case
The rate of interest is 15 % which is 3 / 20.
Read more: Best study timetable to enhance your NID preparation
So, this means that 3 is the interest amount and 20 will be the principal amount.
This means that if you have invested Rs. 20 then after 1 year you will get Rs. 3 as an interest earned.
So, now we have to find in what time the money which is invested will be doubled. Which means in what time you will get that much interest that will be equal to the invested money.
Now, we will calculate the time that in how many years the invested money is doubled.
⇒ Invested money = interest earned per annum X ‘n’ number of time
⇒ 20 = 3 x n
⇒ n = 20 / 3
⇒ n = 6.66 years
⇒ n = 7 years approx.
So, in 7 years the money invested will be doubled when the interest earned at a rate of 15% per annum.
These are some of the questions mentioned below to show you how you can solve simple interest questions for NID examination. These questions will help you to easily understand the format to solve the simple interest questions for NID examination.
By solving these questions you will find that the simple interest questions are easy to solve and very scoring. You will get every trick and method to solve simple interest questions easily. So practice these questions and enhance your preparation.
Read more: Important questions for the NID CAT exam
Question 1: Find the simple interest on Rs. 7,200 at 8% per annum for 10 months.
Answer: (a) Rs. 480
Explanation:
To Given: Principal amount - Rs. 7,200
Rate of interest = 8% per annum
Time = 10 months
To find: Simple Interest?
Solution: here principal = Rs. 7,200
Rate of interest = 8% per annum
Time = 10/12 years = ⅚ years
⇒ Simple Interest = (Principal x Time x Rate of Interest / 100)
⇒ SI = (P x T x R / 100)
⇒ Simple Interest = (7200 x ⅚ x 8 / 100)
⇒ Simple Interest = 60 x 8
⇒ Simple Interest = Rs. 480.
Read more: Important questions for the NID GAT exam
Therefore, the simple interest is Rs. 480.
Question 2: Find the simple interest on Rs, 14,600 at 8 ¼ % per annum for the period from 10th March, 2009 to 17th June, 2009.
Answer: (e) None of these
Explanation:
To given: principal amount = Rs. 14,600
Rate of interest = 8 ¼ %
Time = 10th March, 2009 to 17th June, 2009.
To find: Simple interest?
Solution: Here
Principal amount = Rs. 14,600
Rate of interest = 8 ¼ % = 33/4 % per annum
Time = March + April + May + June
⇒ Time = 21 days + 30 days + 31 days + 17 days
⇒ Time = 99 days.
⇒ Simple Interest = (Principal x Time x Rate of Interest / 100)
⇒ SI = (P x T x R / 100)
⇒ Simple Interest = (14600 x 33/4 x 99/365 / 100)
⇒ Simple Interest = (14600 x 33/4 x 99/365 x 1/100)
⇒ Simple Interest = (146 x 33/4 x 99/365)
⇒ Simple Interest = Rs. 326.70
Therefore, the simple interest is Rs. 326.70
Question 3: Find the amount on a principal of Rs. 3,600 for 2 years and 9 months at a rate of 8 ⅓ % per annum.
Answer: (b) Rs. 4,425
Explanation:
To Given: Principal amount = Rs. 3,600
Rate of Interest = 8 ⅓ % per annum
Time = 2 years and 9 months
To Find: Simple Interest and Total Amount
Solution: Here
Principal Amount = Rs. 3,600
Rate of Interest = 8 ⅓ % = 25/3 %
Time = 2 years and 9 months
⇒ Time = (2 x 12) + 9 / 12 years
⇒ Time = 33/12 years
⇒ Time = 11/4 years
⇒ Simple Interest = (Principal x Time x Rate of interest / 100)
⇒ SI = (P x T x R / 100)
⇒ Simple Interest = (3600 x 11/4 x 25/3 / 100)
⇒ Simple Interest = (3600 x 11/4 x 25/3 x 1/100)
⇒ Simple Interest = (36 x 11/4 x 25/3)
⇒ Simple Interest = (3 x 11 x 25)
⇒ Simple Interest = Rs. 825
Therefore, the Simple Interest is Rs. 825.
⇒ Total Amount to be paid = Principal Amount + Simple Interest
⇒ Total Amount to be paid = P + SI
⇒ Total amount to be paid = 3600 + 825
⇒ Total Amount to be paid = Rs. 4,425.
Therefore, the Total Amount to be paid is Rs. 4,425
Question 4: The simple interest earned on a certain sum is Rs. 1,560 at the rate 8% per annum in 2 years. Find the sum.
Answer: (c) Rs. 9750
Explanation:
To Given: Simple Interest = Rs. 1,560
Rate of Interest = 8% per annum
Time = 2 years
To find: the sum or Principal Amount
Solution: Here
Simple Interest = Rs. 1,560
Rate of Interest = 8% per annum
Time = 2 years
Let the principal amount be 𝒙
⇒ Simple Interest = (Principal x Time x Rate of Interest / 100)
⇒ Simple Interest = (P x T x R / 100)
⇒ 1560 = (𝒙 x 2 x 8/100)
⇒ 1560 = (𝒙 x 2 x 2/25)
⇒ 1560 = 4𝒙 / 25
⇒ 𝒙 = 1560 x 25 / 4
⇒ 𝒙 = 9750
Therefore, the Principal Amount = Rs. 9,750
Question 5: A certain sum amounts to Rs. 7,080 in 2 years and to Rs. 8,430 in 4 ½ year at simple interest. Find the rate of interest.
Answer: (d) 9%
Explanation:
To given: Amount in 4 ½ years = Rs. 8,430
Amount in 2 years = Rs. 7,080
To Find: Rate of Interest?
Solution: Here
Amount in 4 ½ years = Rs. 8,430
Amount in 2 years = Rs. 7,080
First we will find simple interest for 2 ½ years
Then after calculating simple interest for 2 ½ years
We will calculate simple interest for 2 years
⇒ Simple Interest for 2 ½ years = (Amount in 4 ½ years - Amount in 2 years)
⇒ Simple interest for 2 ½ years = (8430 - 7080)
⇒ Simple Interest for 2 ½ years = Rs. 1,350
⇒ Simple Interest for 2 years = (1350 x ⅖ x 2)
⇒ Simple Interest for 2 years = (270 x 4)
⇒ Simple Interest for 2 years = Rs.1,080
Now, we will find the principal amount.
⇒ Principal = (Amount in 2 years) - (Simple Interest for 2 years)
⇒ Principal = (7080) - (1080)
⇒ Principal = (7080 - 1080)
⇒ Principal = Rs. 6,000
After calculating the Principal amount,
we will calculate the rate of interest
Now,
Principal = Rs. 6,000
Time = 2 years
Simple Interest = Rs. 1,080
⇒ Rate of Interest = (100 x Simple Interest / Principal x Time)
⇒ Rate of Interest = (100 x SI / P x T)
⇒ Rate of Interest = (100 x 1080 / 6000 x 2)
⇒ Rate of Interest = (108 / 12)
⇒ Rate of Interest = 9 % per annum.
Therefore, the rate of interest = 9 % per annum.
Question 6: At what rate will Rs. 14,400 give Rs. 4,032 as simple interest in 3 years and 6 months?
Answer: (a) 8%
Explanation:
To Given: Principal = Rs. 14,400
Time = 3 ½ years
Simple Interest = Rs. 4,032
To Find: Rate of interest per annum.
Solution: Here
Principal = Rs. 14,400
Simple Interest = Rs. 4,032
Time = 3 ½ years
Rate of interest per annum = ?
⇒ Time = 3 ½ years
⇒ Time = 7/2 years
Now, we will calculate the rate of interest per annum.
⇒ Rate of interest per annum = (100 x Simple Interest / Principal x Time)
⇒ R = (100 x SI / P x T)
⇒ Rate of Interest = (100 x 4032 / 14400 x ⅖)
⇒ Rate of Interest = (100 x 4032 x 2 / 14400 x 7)
⇒ Rate of Interest = (8064 / 1008)
⇒ Rate of Interest = 8 % per annum
Therefore, the rate of interest per annum = 8%
Question 7: In what time will a sum double itself at 8% per annum simple interest?
Answer: (c) 12 ½ year
Explanation:
To given: Rate of simple interest is 8%
To find: In what time the principal amount will be doubled..
Solution:
First we will convert percentage into fraction
So,
5% = 1/20
10% = 1/10
8% = 2/25
When you have converted percentage into fraction
It means
That 8% = 2 / 25
As we have mentioned above, if the rate of interest is given in percentage and we have converted that into a fraction then the numerator will be assumed as the interest amount and the denominator will be assumed as the principal amount.
So, in this case
The rate of interest is 8 % which is 2 / 25.
So, this means that 2 is the interest amount and 25 will be the principal amount.
This means that if you have invested Rs. 25 then after 1 year you will get Rs. 2 as an interest earned.
So, now we have to find in what time the money which is invested will be doubled. Which means in what time you will get that much interest that will be equal to the invested money.
Now, we will calculate the time that in how many years the invested money is doubled.
⇒ Invested money = interest earned per annum X ‘n’ number of time
⇒ 25 = 2 x n
⇒ n = 25 / 2
⇒ n = 12.5 years
⇒ n = 12 ½ years
So, in 12 ½ years the money invested will be doubled when the interest earned at a rate of 8% per annum.
OR
We can calculate time by one more method i.e.
Let the sum be Rs. 100
It is given in the question that amount is double of the sum
So,
Amount be Rs. 200
⇒ Simple Interest = Amount - Principal
⇒ Simple Interest = 200 - 100
⇒ Simple Interest = Rs. 100
Now,
⇒Time = (100 x Simple Interest / Principal x Rate of Interest)
⇒ Time = (100 x SI / P x R)
⇒ Time = (100 x 100 / 100 x 8)
⇒ Time = 100 / 8
⇒ Time = 25 / 2 years
⇒ Time = 12 ½ years
Therefore, in 12 ½ years the sum will be doubled itself.
Question 8: At what rate will a sum increase by 25% in 2 years at Simple Interest?
Answer: (a) 12 ½ %
Explanation:
To Find: Rate of Interest.
Solution:
Let the sum be Rs. 100
Then, amount will be 25% extra of the sum
So, the amount = Rs. 125
Now, according to the above information we will calculate simple interest.
⇒ Simple Interest = Amount - Principal
⇒ Simple Interest = A - P
⇒ Simple Interest = 125 - 100
⇒ Simple Interest = Rs. 25
Now, after calculating simple interest we will calculate the rate of interest per annum.
Here,
Principal = Rs. 100
Amount = Rs. 125
Simple Interest = Rs. 25
Time = 2 years
⇒ Rate of Interest = (100 x Simple Interest / Principal x Time)
⇒ Rate of Interest = (100 x SI / P x T)
⇒ Rate of Interest = (100 x 25 / 100 x 2)
⇒ Rate of Interest = 25 / 2
⇒ Rate of Interest = 12 ½ % per annum.
Therefore, the rate of interest = 12 ½ % per annum.
Question 9: At what time would Rs. 5,000 amount to Rs. 5,800 at 8% per annum simple interest?
Answer: (d) 2 year.
Explanation:
To Given: Principal = Rs. 5,000
Amount = Rs. 5,800
Rate of Interest = 8% per annum
To find: Time =?
Solution: Here
Principal = Rs. 5,000
Amount = Rs. 5,800
Rate of Interest = 8% per annum.
Now,
We will calculate Simple Interest
⇒ Simple Interest = Amount - Principal
⇒ Simple Interest = A - P
⇒ Simple Interest = 5800 - 5000
⇒ Simple Interest = Rs. 800
After calculating simple interest,
We have Principal = Rs. 5,000
Amount = Rs. 5,800
Rate of Interest = 8% per annum
Simple Interest = Rs. 800
Now, we have to calculate Time
⇒ Time = (100 x Simple Interest / Principal x Rate of Interest)
⇒ T = (100 x SI / P x R)
⇒ Time = (100 x 800 / 5000 x 8)
⇒ Time = (10 / 5)
⇒ Time = 2 years
Therefore, the time = 2 years.
Question 10: At what time would a sum double itself at 12 ½ % per annum simple interest?
Answer: (d) 8 year
Explanation:
To Given: Rate of simple interest is 12 ½ %
To find: In what time the principal amount will be doubled..
Solution:
We can calculate time by one more method i.e.
Let the sum be Rs. 100
It is given in the question that amount is double of the sum
So,
Amount be Rs. 200
⇒ Simple Interest = Amount - Principal
⇒ SI = A - P
⇒ Simple Interest = 200 - 100
⇒ Simple Interest = Rs. 100
Now,
⇒Time = (100 x Simple Interest / Principal x Rate of Interest)
⇒ Time = (100 x SI / P x R)
⇒ Time = (100 x 100 / 100 x 25/2)
⇒ Time = (100 x 100 x 2 / 100 x 25)
⇒ Time = 200 / 25
⇒ Time = 8 years
⇒ Time = 8 years
Therefore, in 8 years the sum will double itself.
Question 11: At what time would Rs. 5,400 at 8% per annum yield the simple interest as Rs. 2,400 at 9% per annum in 4 year?
Answer: (a) 2 year
Explanation:
To Given: Principal = Rs. 2,400
Time = 4 year
Rate of Interest = 9% per annum
To Find: Simple Interest =?
Time =?
Solution:
We will have to calculate Time and simple interest
First we will calculate simple interest.
Here Principal = Rs. 2,400
Time = 4 year
Rate of Interest = 9% per annum
⇒ Simple Interest = Principal x Time x Rate of Interest / 100)
⇒ SI = (P x T x R / 100)
⇒ Simple Interest = (2400 x 4 x 9 / 100)
⇒ Simple Interest = 24 x 4 x 9
⇒ simple Interest = Rs. 864
After calculating we will calculate time
Here principal = Rs. 5,400
Simple Interest = Rs. 864
Rate of Interest = 8% per annum
⇒ Time = (100 x Simple Interest / Principal x Rate of Interest)
⇒ Time = (100 x 864 / 5400 x 8)
⇒ Time = (864 / 432)
⇒ Time = 2 year
Question 12: The difference between the simple interest received from two different sources on Rs. 5,200 for 2 ½ year is Rs. 65. The difference between their rates of interest is.
Answer: (a) 0.5%
Explanation:
To Given: Principal = Rs. 5,200
Time = 2 ½ year
Simple Interest = Rs. 65
To Find: the difference between their rates of interest =?
Solution: Here
Principal = Rs. 5,200
Time = 2 ½ year
Simple Interest = Rs. 65
Let the rate of interest be 𝒙 % per annum
Let the rate of interest be 𝒚 % per annum
Then,
⇒ Simple Interest = (Principal x Time x Rate of Interest / 100) - (Principal x Time x Rate of Interest / 100)
⇒ 65 = (5200 x 5/2 x 𝒙/100) - (5200 x 5/2 x 𝒚/100)
⇒ 65 = (26 x 5𝒙) - (26 x 5𝒚)
⇒ 65 = (130𝒙) - (130𝒚)
⇒ 65 = 130 (𝒙 - 𝒚)
⇒ 65/130 = (𝒙 - 𝒚)
⇒ ½ = (𝒙 - 𝒚)
⇒ 0.5 % = (𝒙 - 𝒚)
Hence, the required difference is 0.5%
Question 13: A sum of Rs. 8,000 was lent partly at 7% and partly at 9% simple interest. If the total annual interest is Rs. 620. The ratio in which the money was lent at given rates is.
Answer: (a) 5 : 3
Explanation:
To given: principal = Rs. 8,000
Simple interest = Rs. 620
Rate of Interest = 7% and 9%
To Find: the ratio in which the money was lent at given rates
Solution:
Here
Principal amount = Rs. 8,000
Simple Interest = Rs. 620
Rate of Interest = 7% and 9%
Let the money invested at the two rates be Rs. 𝒙 and Rs. (8000 - 𝒙)
Then,
⇒ (𝒙 x 7 x 1 / 100) + (8000 - 𝒙) x 9/100 x 1 = 620
⇒ (7𝒙 / 100) + 720 - 9𝒙 / 100 = 620
⇒ 2𝒙 / 100 = 720 - 620
⇒ 2𝒙 / 100 = 100
⇒ 2𝒙 = 100 x 100
⇒ 2𝒙 = 10000
⇒ 𝒙 = 10000 / 2
⇒ 𝒙 = Rs. 5,000
Money invested is in the ratio = 𝒙 : (8000 - 𝒙)
⇒ Money invested is in the ratio = 5000 : (8000 - 5000)
⇒ Money invested is in the ratio = 5000 : 3000
⇒ Money invested is in the ratio = 5 : 3
Question 14: A man buys a music system valued at Rs. 8,000. He pays Rs. 3,500 at once and the rest 18 months later on which he is charged simple interest at the rate of 8% per annum. Find the total amount he pays for the music system.
Answer: (b) Rs. 8,540
Explanation:
To given: Cost of the music system = Rs. 8,000
Money paid at once = Rs. 3,500
Time = 18 months
Rate of Interest = 8 % per annum
To find: the total amount he pays for the music system.
Solution: Here
Cost of the music system = Rs. 8,000
Money paid at once = Rs. 3,500
Time = 18 months
Rate of Interest = 8 % per annum
⇒ Time = 18 months = 18 / 12
⇒ Time = 1 ½ year
First we will calculate the money left.
Cost of the music system = Rs. 8,000
Money paid at once = Rs. 3,500
⇒ Money left = 8,000 - 3,500
⇒ Money left = Rs. 4,500
Now we will calculate simple interest,
Here Principal amount = Rs. 4,500
Time = 1 ½ year = 3 / 2 year
Rate of Interest = 8% per annum
⇒ Simple Interest = (Principal x Time x Rate / 100)
⇒ SI = (P x R x T / 100)
⇒ Simple Interest = (4500 x 3/2 x 8 / 100)
⇒ Simple Interest = (45 x 3 x 4)
⇒ Simple Interest = Rs. 540
⇒ Money to be paid at the end = 4500 + 540
⇒ Money to be paid at the end = Rs. 5,040
Cost of music system = 3500 + 5040
⇒ Cost of music system = Rs. 8,540
Therefore, the cost of the music system = Rs. 8,540
Question 15: A sum of Rs. 5,000 was lent at 6% per annum and Rs. 6,000 at 7% per annum simple interest. After what time would the total interest be Rs. 1,080?
Answer: (c) 1 ½ year
Explanation:
To Given: Principal ₁ = Rs. 5,000
Principal ₂ = Rs. 6,000
Rate of interest ₁ = 6%
Rate of interest ₂ = 7%
To Find: After what time would the total interest be Rs. 1,080?
Solution:
Here Principal ₁ = Rs. 5,000
Principal ₂ = Rs. 6,000
Rate of interest ₁ = 6%
Rate of interest ₂ = 7%
Let the time be 𝒙 year.
We will calculate simple interest by taking both the principal and rate of interest.
⇒ Simple Interest ₁ = (Principal ₁ x Time x Rate ₁ / 100)
⇒ SI₁ = (P ₁ x R ₁ x T / 100)
⇒ Simple Interest ₁ = (5000 x 𝒙 x 6 / 100)
⇒ Simple Interest ₁ = (50 x 𝒙 x 6)
⇒ Simple Interest ₁ = 300𝒙
⇒ Simple Interest ₂ = (Principal ₂ x Time x Rate ₂ / 100)
⇒ SI ₂ = (P ₂ x R ₂ x T / 100)
⇒ Simple Interest ₂ = (6000 x 𝒙 x 7 / 100)
⇒ Simple Interest ₂ = (60 x 𝒙 x 7)
⇒ Simple Interest ₂ = 420𝒙
⇒ Rate of interest = Rate of interest ₁ + Rate of interest ₂
⇒ 1080 = (300𝒙 + 420𝒙)
⇒ 1080 = 720𝒙
⇒ 1080 / 720 = 𝒙
⇒ 3/2 = 𝒙
⇒ 𝒙 = 1 ½ year
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Updated On : May 9, 2022
Simple interest is interest calculated on the principal portion of a loan or the original contribution to a saving account. Simple interest does not compound, meaning that an account holder will only gain interest on the principal, and a borrower will never have to pay interest on interest already accrued.
It is a sum which is paid by the borrower to the lender for using the money for a specific period of time. The money borrowed is the principal.
The rate at which the interest is calculated on the principal is called the rate of interest. The time for which the money is borrowed is the time and the total sum of principal and interest is called amount.
Simple Interest is the interest calculated on the original principal at any rate of interest for any period of time, then it is called simple interest.
If P = Principal,
R = Rate percent per annum,
T = Number of years,
SI = Simple Interest and
A = Amount
Then,
73 days = ⅕ yr
146 days = ⅖ yr
219 days = ⅗ yr
292 days = ⅘ yr
Download Free Practice Question Papers for NID Exam by CreativeEdge
The formula of simple interest is:
Simple Interest = Principal x Time Period x Rate of Interest / 100
Principal = 100 x Simple Interest / Rate of Interest x Time period
Rate of Interest = 100 x Simple Interest / Principal x Time Period
Time = 100 x Simple Interest / Principal x Rate of Interest
Amount = Principal x Simple Interest
Here, the interest is calculated on the original principal, i.e., the principal, to calculate the interest it remains constant throughout the time period. The interest earned on the principal is not taken into account for the purpose of calculating interest for later years.
In this article, you will get to know how to solve simple interest problems for NID.
The key to success in the exam is planning a well-structured study plan for NID and executing it effectively.
Before solving the simple interest problems for NID we should know all the parameters which will help in solving simple interest problems.
The fractional value of 25% is ¼, the fractional value of 20% is ⅕, and the fractional value of 33.33% is ⅓.
For example: In a question the rate of interest is given as 8.33% per annum so it will be 1/12 in the fractional form. Here that 1/12 means that 12 the denominator is the principal amount and 1 the numerator is the interest when you have received or paid on the principal amount in one year.
To help you get an idea about the type of questions asked in the exam, we have curated few sample questions from the previous year's NID Question papers.
Let us understand with an example:
For example 1: Sagar borrows Rs. 50,000 from a bank for 5 years. What is the rate of simple interest charged by the bank if after 5 years Sagar had to pay Rs. 66,000 to the bank?
Answer: 6.4 %
Solution:
This question can be solved in a fraction of seconds by using the simple interest formula but we will solve it by a different method so that you can easily understand the simple interest concept.
Once you have understood the simple interest concept you can easily solve any kind of question related to simple interest in seconds.
To given: sagar has borrowed rs. 50,000 from a bank for 5 years
And, after 5 years, Sagar will pay rs. 66,000 to the bank.
To find: the rate of interest on which sagar had borrowed the money from bank
Let us find out,
Sagar had borrowed Rs. 50,000 and he has to pay Rs. 66,000 after 5 years
Read more: Previous year exam analysis for NID entrance exam
So,
In this case we can say that the additional amount which sagar is paying is our simple interest
So, we will see the additional amount by subtracting Rs. 50,000 from Rs. 66,000.
The additional amount which he will pay as a simple interest will be 66,000 - 50,000 = 16,000.
So, the simple interest for 5 years will be Rs. 16,000
Now, we have to find at what rate of interest per annum he is paying the interest to the bank
So, the total simple interest for 5 years is Rs. 16,000
So the simple interest for 1 year will be 16000/5 = 3,200
Rate of interest = simple interest is what percentage of principal per year
Now, see below
Simple interest = Rs. 3,200 for 1 year
Principal amount = Rs. 50,000
Rate of interest = simple interest of 1 year / principal amount * 100
Rate of interest = 3200 / 50000 x 100
Rate of interest = 6.4 %
Read more: Important questions with answers for the NID CAT exam
So, the rate of interest on which sagar will pay the interest to the bank every year will be 6.4%
Let us understand the concept more by solving one more example
For Example 2:
After how many years would an amount double itself at 15% rate of simple interest?
Answer: in 7 years approximately the invested amount will be doubled.
Explanation:
To given: rate of simple interest 15%
To find: In what time the principal amount will be doubled..
Solution:
First we will convert percentage into fraction
So,
5% = 1/20
10% = 1/10
15% = 3/20
When you have converted percentage into fraction
It means
That 15% = 3 / 20
As we have mentioned above, if the rate of interest is given in percentage and we have converted that into a fraction then the numerator will be assumed as the interest amount and the denominator will be assumed as the principal amount.
So, in this case
The rate of interest is 15 % which is 3 / 20.
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So, this means that 3 is the interest amount and 20 will be the principal amount.
This means that if you have invested Rs. 20 then after 1 year you will get Rs. 3 as an interest earned.
So, now we have to find in what time the money which is invested will be doubled. Which means in what time you will get that much interest that will be equal to the invested money.
Now, we will calculate the time that in how many years the invested money is doubled.
⇒ Invested money = interest earned per annum X ‘n’ number of time
⇒ 20 = 3 x n
⇒ n = 20 / 3
⇒ n = 6.66 years
⇒ n = 7 years approx.
So, in 7 years the money invested will be doubled when the interest earned at a rate of 15% per annum.
These are some of the questions mentioned below to show you how you can solve simple interest questions for NID examination. These questions will help you to easily understand the format to solve the simple interest questions for NID examination.
By solving these questions you will find that the simple interest questions are easy to solve and very scoring. You will get every trick and method to solve simple interest questions easily. So practice these questions and enhance your preparation.
Read more: Important questions for the NID CAT exam
Question 1: Find the simple interest on Rs. 7,200 at 8% per annum for 10 months.
Answer: (a) Rs. 480
Explanation:
To Given: Principal amount - Rs. 7,200
Rate of interest = 8% per annum
Time = 10 months
To find: Simple Interest?
Solution: here principal = Rs. 7,200
Rate of interest = 8% per annum
Time = 10/12 years = ⅚ years
⇒ Simple Interest = (Principal x Time x Rate of Interest / 100)
⇒ SI = (P x T x R / 100)
⇒ Simple Interest = (7200 x ⅚ x 8 / 100)
⇒ Simple Interest = 60 x 8
⇒ Simple Interest = Rs. 480.
Read more: Important questions for the NID GAT exam
Therefore, the simple interest is Rs. 480.
Question 2: Find the simple interest on Rs, 14,600 at 8 ¼ % per annum for the period from 10th March, 2009 to 17th June, 2009.
Answer: (e) None of these
Explanation:
To given: principal amount = Rs. 14,600
Rate of interest = 8 ¼ %
Time = 10th March, 2009 to 17th June, 2009.
To find: Simple interest?
Solution: Here
Principal amount = Rs. 14,600
Rate of interest = 8 ¼ % = 33/4 % per annum
Time = March + April + May + June
⇒ Time = 21 days + 30 days + 31 days + 17 days
⇒ Time = 99 days.
⇒ Simple Interest = (Principal x Time x Rate of Interest / 100)
⇒ SI = (P x T x R / 100)
⇒ Simple Interest = (14600 x 33/4 x 99/365 / 100)
⇒ Simple Interest = (14600 x 33/4 x 99/365 x 1/100)
⇒ Simple Interest = (146 x 33/4 x 99/365)
⇒ Simple Interest = Rs. 326.70
Therefore, the simple interest is Rs. 326.70
Question 3: Find the amount on a principal of Rs. 3,600 for 2 years and 9 months at a rate of 8 ⅓ % per annum.
Answer: (b) Rs. 4,425
Explanation:
To Given: Principal amount = Rs. 3,600
Rate of Interest = 8 ⅓ % per annum
Time = 2 years and 9 months
To Find: Simple Interest and Total Amount
Solution: Here
Principal Amount = Rs. 3,600
Rate of Interest = 8 ⅓ % = 25/3 %
Time = 2 years and 9 months
⇒ Time = (2 x 12) + 9 / 12 years
⇒ Time = 33/12 years
⇒ Time = 11/4 years
⇒ Simple Interest = (Principal x Time x Rate of interest / 100)
⇒ SI = (P x T x R / 100)
⇒ Simple Interest = (3600 x 11/4 x 25/3 / 100)
⇒ Simple Interest = (3600 x 11/4 x 25/3 x 1/100)
⇒ Simple Interest = (36 x 11/4 x 25/3)
⇒ Simple Interest = (3 x 11 x 25)
⇒ Simple Interest = Rs. 825
Therefore, the Simple Interest is Rs. 825.
⇒ Total Amount to be paid = Principal Amount + Simple Interest
⇒ Total Amount to be paid = P + SI
⇒ Total amount to be paid = 3600 + 825
⇒ Total Amount to be paid = Rs. 4,425.
Therefore, the Total Amount to be paid is Rs. 4,425
Question 4: The simple interest earned on a certain sum is Rs. 1,560 at the rate 8% per annum in 2 years. Find the sum.
Answer: (c) Rs. 9750
Explanation:
To Given: Simple Interest = Rs. 1,560
Rate of Interest = 8% per annum
Time = 2 years
To find: the sum or Principal Amount
Solution: Here
Simple Interest = Rs. 1,560
Rate of Interest = 8% per annum
Time = 2 years
Let the principal amount be 𝒙
⇒ Simple Interest = (Principal x Time x Rate of Interest / 100)
⇒ Simple Interest = (P x T x R / 100)
⇒ 1560 = (𝒙 x 2 x 8/100)
⇒ 1560 = (𝒙 x 2 x 2/25)
⇒ 1560 = 4𝒙 / 25
⇒ 𝒙 = 1560 x 25 / 4
⇒ 𝒙 = 9750
Therefore, the Principal Amount = Rs. 9,750
Question 5: A certain sum amounts to Rs. 7,080 in 2 years and to Rs. 8,430 in 4 ½ year at simple interest. Find the rate of interest.
Answer: (d) 9%
Explanation:
To given: Amount in 4 ½ years = Rs. 8,430
Amount in 2 years = Rs. 7,080
To Find: Rate of Interest?
Solution: Here
Amount in 4 ½ years = Rs. 8,430
Amount in 2 years = Rs. 7,080
First we will find simple interest for 2 ½ years
Then after calculating simple interest for 2 ½ years
We will calculate simple interest for 2 years
⇒ Simple Interest for 2 ½ years = (Amount in 4 ½ years - Amount in 2 years)
⇒ Simple interest for 2 ½ years = (8430 - 7080)
⇒ Simple Interest for 2 ½ years = Rs. 1,350
⇒ Simple Interest for 2 years = (1350 x ⅖ x 2)
⇒ Simple Interest for 2 years = (270 x 4)
⇒ Simple Interest for 2 years = Rs.1,080
Now, we will find the principal amount.
⇒ Principal = (Amount in 2 years) - (Simple Interest for 2 years)
⇒ Principal = (7080) - (1080)
⇒ Principal = (7080 - 1080)
⇒ Principal = Rs. 6,000
After calculating the Principal amount,
we will calculate the rate of interest
Now,
Principal = Rs. 6,000
Time = 2 years
Simple Interest = Rs. 1,080
⇒ Rate of Interest = (100 x Simple Interest / Principal x Time)
⇒ Rate of Interest = (100 x SI / P x T)
⇒ Rate of Interest = (100 x 1080 / 6000 x 2)
⇒ Rate of Interest = (108 / 12)
⇒ Rate of Interest = 9 % per annum.
Therefore, the rate of interest = 9 % per annum.
Question 6: At what rate will Rs. 14,400 give Rs. 4,032 as simple interest in 3 years and 6 months?
Answer: (a) 8%
Explanation:
To Given: Principal = Rs. 14,400
Time = 3 ½ years
Simple Interest = Rs. 4,032
To Find: Rate of interest per annum.
Solution: Here
Principal = Rs. 14,400
Simple Interest = Rs. 4,032
Time = 3 ½ years
Rate of interest per annum = ?
⇒ Time = 3 ½ years
⇒ Time = 7/2 years
Now, we will calculate the rate of interest per annum.
⇒ Rate of interest per annum = (100 x Simple Interest / Principal x Time)
⇒ R = (100 x SI / P x T)
⇒ Rate of Interest = (100 x 4032 / 14400 x ⅖)
⇒ Rate of Interest = (100 x 4032 x 2 / 14400 x 7)
⇒ Rate of Interest = (8064 / 1008)
⇒ Rate of Interest = 8 % per annum
Therefore, the rate of interest per annum = 8%
Question 7: In what time will a sum double itself at 8% per annum simple interest?
Answer: (c) 12 ½ year
Explanation:
To given: Rate of simple interest is 8%
To find: In what time the principal amount will be doubled..
Solution:
First we will convert percentage into fraction
So,
5% = 1/20
10% = 1/10
8% = 2/25
When you have converted percentage into fraction
It means
That 8% = 2 / 25
As we have mentioned above, if the rate of interest is given in percentage and we have converted that into a fraction then the numerator will be assumed as the interest amount and the denominator will be assumed as the principal amount.
So, in this case
The rate of interest is 8 % which is 2 / 25.
So, this means that 2 is the interest amount and 25 will be the principal amount.
This means that if you have invested Rs. 25 then after 1 year you will get Rs. 2 as an interest earned.
So, now we have to find in what time the money which is invested will be doubled. Which means in what time you will get that much interest that will be equal to the invested money.
Now, we will calculate the time that in how many years the invested money is doubled.
⇒ Invested money = interest earned per annum X ‘n’ number of time
⇒ 25 = 2 x n
⇒ n = 25 / 2
⇒ n = 12.5 years
⇒ n = 12 ½ years
So, in 12 ½ years the money invested will be doubled when the interest earned at a rate of 8% per annum.
OR
We can calculate time by one more method i.e.
Let the sum be Rs. 100
It is given in the question that amount is double of the sum
So,
Amount be Rs. 200
⇒ Simple Interest = Amount - Principal
⇒ Simple Interest = 200 - 100
⇒ Simple Interest = Rs. 100
Now,
⇒Time = (100 x Simple Interest / Principal x Rate of Interest)
⇒ Time = (100 x SI / P x R)
⇒ Time = (100 x 100 / 100 x 8)
⇒ Time = 100 / 8
⇒ Time = 25 / 2 years
⇒ Time = 12 ½ years
Therefore, in 12 ½ years the sum will be doubled itself.
Question 8: At what rate will a sum increase by 25% in 2 years at Simple Interest?
Answer: (a) 12 ½ %
Explanation:
To Find: Rate of Interest.
Solution:
Let the sum be Rs. 100
Then, amount will be 25% extra of the sum
So, the amount = Rs. 125
Now, according to the above information we will calculate simple interest.
⇒ Simple Interest = Amount - Principal
⇒ Simple Interest = A - P
⇒ Simple Interest = 125 - 100
⇒ Simple Interest = Rs. 25
Now, after calculating simple interest we will calculate the rate of interest per annum.
Here,
Principal = Rs. 100
Amount = Rs. 125
Simple Interest = Rs. 25
Time = 2 years
⇒ Rate of Interest = (100 x Simple Interest / Principal x Time)
⇒ Rate of Interest = (100 x SI / P x T)
⇒ Rate of Interest = (100 x 25 / 100 x 2)
⇒ Rate of Interest = 25 / 2
⇒ Rate of Interest = 12 ½ % per annum.
Therefore, the rate of interest = 12 ½ % per annum.
Question 9: At what time would Rs. 5,000 amount to Rs. 5,800 at 8% per annum simple interest?
Answer: (d) 2 year.
Explanation:
To Given: Principal = Rs. 5,000
Amount = Rs. 5,800
Rate of Interest = 8% per annum
To find: Time =?
Solution: Here
Principal = Rs. 5,000
Amount = Rs. 5,800
Rate of Interest = 8% per annum.
Now,
We will calculate Simple Interest
⇒ Simple Interest = Amount - Principal
⇒ Simple Interest = A - P
⇒ Simple Interest = 5800 - 5000
⇒ Simple Interest = Rs. 800
After calculating simple interest,
We have Principal = Rs. 5,000
Amount = Rs. 5,800
Rate of Interest = 8% per annum
Simple Interest = Rs. 800
Now, we have to calculate Time
⇒ Time = (100 x Simple Interest / Principal x Rate of Interest)
⇒ T = (100 x SI / P x R)
⇒ Time = (100 x 800 / 5000 x 8)
⇒ Time = (10 / 5)
⇒ Time = 2 years
Therefore, the time = 2 years.
Question 10: At what time would a sum double itself at 12 ½ % per annum simple interest?
Answer: (d) 8 year
Explanation:
To Given: Rate of simple interest is 12 ½ %
To find: In what time the principal amount will be doubled..
Solution:
We can calculate time by one more method i.e.
Let the sum be Rs. 100
It is given in the question that amount is double of the sum
So,
Amount be Rs. 200
⇒ Simple Interest = Amount - Principal
⇒ SI = A - P
⇒ Simple Interest = 200 - 100
⇒ Simple Interest = Rs. 100
Now,
⇒Time = (100 x Simple Interest / Principal x Rate of Interest)
⇒ Time = (100 x SI / P x R)
⇒ Time = (100 x 100 / 100 x 25/2)
⇒ Time = (100 x 100 x 2 / 100 x 25)
⇒ Time = 200 / 25
⇒ Time = 8 years
⇒ Time = 8 years
Therefore, in 8 years the sum will double itself.
Question 11: At what time would Rs. 5,400 at 8% per annum yield the simple interest as Rs. 2,400 at 9% per annum in 4 year?
Answer: (a) 2 year
Explanation:
To Given: Principal = Rs. 2,400
Time = 4 year
Rate of Interest = 9% per annum
To Find: Simple Interest =?
Time =?
Solution:
We will have to calculate Time and simple interest
First we will calculate simple interest.
Here Principal = Rs. 2,400
Time = 4 year
Rate of Interest = 9% per annum
⇒ Simple Interest = Principal x Time x Rate of Interest / 100)
⇒ SI = (P x T x R / 100)
⇒ Simple Interest = (2400 x 4 x 9 / 100)
⇒ Simple Interest = 24 x 4 x 9
⇒ simple Interest = Rs. 864
After calculating we will calculate time
Here principal = Rs. 5,400
Simple Interest = Rs. 864
Rate of Interest = 8% per annum
⇒ Time = (100 x Simple Interest / Principal x Rate of Interest)
⇒ Time = (100 x 864 / 5400 x 8)
⇒ Time = (864 / 432)
⇒ Time = 2 year
Question 12: The difference between the simple interest received from two different sources on Rs. 5,200 for 2 ½ year is Rs. 65. The difference between their rates of interest is.
Answer: (a) 0.5%
Explanation:
To Given: Principal = Rs. 5,200
Time = 2 ½ year
Simple Interest = Rs. 65
To Find: the difference between their rates of interest =?
Solution: Here
Principal = Rs. 5,200
Time = 2 ½ year
Simple Interest = Rs. 65
Let the rate of interest be 𝒙 % per annum
Let the rate of interest be 𝒚 % per annum
Then,
⇒ Simple Interest = (Principal x Time x Rate of Interest / 100) - (Principal x Time x Rate of Interest / 100)
⇒ 65 = (5200 x 5/2 x 𝒙/100) - (5200 x 5/2 x 𝒚/100)
⇒ 65 = (26 x 5𝒙) - (26 x 5𝒚)
⇒ 65 = (130𝒙) - (130𝒚)
⇒ 65 = 130 (𝒙 - 𝒚)
⇒ 65/130 = (𝒙 - 𝒚)
⇒ ½ = (𝒙 - 𝒚)
⇒ 0.5 % = (𝒙 - 𝒚)
Hence, the required difference is 0.5%
Question 13: A sum of Rs. 8,000 was lent partly at 7% and partly at 9% simple interest. If the total annual interest is Rs. 620. The ratio in which the money was lent at given rates is.
Answer: (a) 5 : 3
Explanation:
To given: principal = Rs. 8,000
Simple interest = Rs. 620
Rate of Interest = 7% and 9%
To Find: the ratio in which the money was lent at given rates
Solution:
Here
Principal amount = Rs. 8,000
Simple Interest = Rs. 620
Rate of Interest = 7% and 9%
Let the money invested at the two rates be Rs. 𝒙 and Rs. (8000 - 𝒙)
Then,
⇒ (𝒙 x 7 x 1 / 100) + (8000 - 𝒙) x 9/100 x 1 = 620
⇒ (7𝒙 / 100) + 720 - 9𝒙 / 100 = 620
⇒ 2𝒙 / 100 = 720 - 620
⇒ 2𝒙 / 100 = 100
⇒ 2𝒙 = 100 x 100
⇒ 2𝒙 = 10000
⇒ 𝒙 = 10000 / 2
⇒ 𝒙 = Rs. 5,000
Money invested is in the ratio = 𝒙 : (8000 - 𝒙)
⇒ Money invested is in the ratio = 5000 : (8000 - 5000)
⇒ Money invested is in the ratio = 5000 : 3000
⇒ Money invested is in the ratio = 5 : 3
Question 14: A man buys a music system valued at Rs. 8,000. He pays Rs. 3,500 at once and the rest 18 months later on which he is charged simple interest at the rate of 8% per annum. Find the total amount he pays for the music system.
Answer: (b) Rs. 8,540
Explanation:
To given: Cost of the music system = Rs. 8,000
Money paid at once = Rs. 3,500
Time = 18 months
Rate of Interest = 8 % per annum
To find: the total amount he pays for the music system.
Solution: Here
Cost of the music system = Rs. 8,000
Money paid at once = Rs. 3,500
Time = 18 months
Rate of Interest = 8 % per annum
⇒ Time = 18 months = 18 / 12
⇒ Time = 1 ½ year
First we will calculate the money left.
Cost of the music system = Rs. 8,000
Money paid at once = Rs. 3,500
⇒ Money left = 8,000 - 3,500
⇒ Money left = Rs. 4,500
Now we will calculate simple interest,
Here Principal amount = Rs. 4,500
Time = 1 ½ year = 3 / 2 year
Rate of Interest = 8% per annum
⇒ Simple Interest = (Principal x Time x Rate / 100)
⇒ SI = (P x R x T / 100)
⇒ Simple Interest = (4500 x 3/2 x 8 / 100)
⇒ Simple Interest = (45 x 3 x 4)
⇒ Simple Interest = Rs. 540
⇒ Money to be paid at the end = 4500 + 540
⇒ Money to be paid at the end = Rs. 5,040
Cost of music system = 3500 + 5040
⇒ Cost of music system = Rs. 8,540
Therefore, the cost of the music system = Rs. 8,540
Question 15: A sum of Rs. 5,000 was lent at 6% per annum and Rs. 6,000 at 7% per annum simple interest. After what time would the total interest be Rs. 1,080?
Answer: (c) 1 ½ year
Explanation:
To Given: Principal ₁ = Rs. 5,000
Principal ₂ = Rs. 6,000
Rate of interest ₁ = 6%
Rate of interest ₂ = 7%
To Find: After what time would the total interest be Rs. 1,080?
Solution:
Here Principal ₁ = Rs. 5,000
Principal ₂ = Rs. 6,000
Rate of interest ₁ = 6%
Rate of interest ₂ = 7%
Let the time be 𝒙 year.
We will calculate simple interest by taking both the principal and rate of interest.
⇒ Simple Interest ₁ = (Principal ₁ x Time x Rate ₁ / 100)
⇒ SI₁ = (P ₁ x R ₁ x T / 100)
⇒ Simple Interest ₁ = (5000 x 𝒙 x 6 / 100)
⇒ Simple Interest ₁ = (50 x 𝒙 x 6)
⇒ Simple Interest ₁ = 300𝒙
⇒ Simple Interest ₂ = (Principal ₂ x Time x Rate ₂ / 100)
⇒ SI ₂ = (P ₂ x R ₂ x T / 100)
⇒ Simple Interest ₂ = (6000 x 𝒙 x 7 / 100)
⇒ Simple Interest ₂ = (60 x 𝒙 x 7)
⇒ Simple Interest ₂ = 420𝒙
⇒ Rate of interest = Rate of interest ₁ + Rate of interest ₂
⇒ 1080 = (300𝒙 + 420𝒙)
⇒ 1080 = 720𝒙
⇒ 1080 / 720 = 𝒙
⇒ 3/2 = 𝒙
⇒ 𝒙 = 1 ½ year
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