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KUMAR SHUBHAM

· started a discussion

· 1 Months ago

ci (Question:465724.0)

question no-1
half yearly is given in question but you take time for 2 years

Question:
A certain sum, invested at 4% per annum at compound interest, compounded half-yearly, amounts to Rs.7,803 at the end of one year. Find the sum.
Options:
A) Rs.7,000
B) Rs.7,200
C) Rs.7,500
D) Rs.7,700
Solution:

Ans: (c)

Let the sum be Rs.P.

As, the interest is compounded half-yearly,

∴ R = 2%, T = 2 half years

∴ A = \(P\left ( 1+\cfrac{R}{100} \right )^T\)

\(⇒ 7803 = P\left ( 1+\cfrac{2}{100} \right )^2\)

\(⇒ 7803 = P\left ( 1+\cfrac{1}{50} \right )^2\)

\(⇒ 7803 = P × \cfrac{51}{50} × \cfrac{51}{50}\)

\(⇒ P = \cfrac{7803 × 50 × 50}{51 ×51}\ \ = Rs.7500\)

Alternatively :-

If interest is compounded half- yearly rate will be 2%

C.I. for 2 years = 4.04%

Principal = \(\cfrac{7803}{104.04}× 100\) = Rs.7500

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