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p

· started a discussion

· 1 Months ago

doubt (Question:458344.0)

how you got 21 as rate in the short cut trick

Question:

A sum of money is lent out at compound interest rate of 20% per annum for 2 years. It would fetch Rs. 482 more if interest is compounded half-yearly. Find the sum.

Options:
A) Rs. 20,000
B) Rs. 24,000
C) Rs. 28,000
D) Can’t be determined
Solution:


Let the sum be Rs.P

C.I. when interest is compounded yearly = P \(\big[ 1+\cfrac{20}{100} \big]^2 -P\)

CI when interest is compounded half-yearly = P \(\big[ 1+\cfrac{10}{200} \big]^4 -P\)

Now, we have,

P \(\big[ 1+\cfrac{10}{100} \big]^4 \)- P  \(\big[ 1+\cfrac{20}{100} \big]^2 \)= 482

⇒ P[(1.1)4 - (1.2)2] = 482

⇒ P[(1.1)2 - (1.2)] [(1.1)2 + (1.2)]

= 482

⇒ P[(1.21 - 1.2) (1.21 + 1.2)] = 482

⇒ P[(0.01) (2.41)] = 482

∴ P = \(\cfrac{482}{2.41\times0.01}\)

∴ P =  Rs. 20,000  

or short trick method:


Knowledge Expert

· commented

· 1 Months ago

Dear Student,
Kindly have a look at the solution given below
The effective rate of Interest for 1st year when rate of interest is compounded half-yearly=10+10+(10*10)/100=21 %
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