Question : If interest is being compounded half-yearly, then what sum will amount to INR 51,840 in 2 years at the rate of 40% per annum on compound interest?
Option 1: INR 25,000
Option 2: INR 15,000
Option 3: INR 20,000
Option 4: INR 30,000

Question

Question : The difference between the compound interest and the simple interest on a certain sum of money at 10% per annum for 2 years is INR 200. What is the sum of money, if in the case of compound interest, interest is compounded annually?

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Answer 1

Correct Answer: INR 25,000

Solution : Amount = INR 51,840
Term, $n$ = 2 years
Rate, $R$ = 40%
Let $P$ be the principal sum.
When compounded half-yearly,
Amount = $P (1 + \frac{R}{200})^{2 n}$
⇒ 51840 = $P (1 + \frac{40}{200})^{2 \times 2}$
⇒ 51840 = $P (1 + \frac{1}{5})^{4}$
⇒ 51840 = $P (\frac{6}{5})^{4}$
⇒ $P = \frac{51840 \times 625}{36 \times 36} = 25000$
Hence, the correct answer is INR 25,000.

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Question : If interest is being compounded half-yearly, then what sum will amount to INR 51,840 in 2 years at the rate of 40% per annum on compound interest?Option 1: INR 25,000Option 2: INR 15,000Option 3: INR 20,000Option 4: INR 30,000

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Question : If interest is being compounded half-yearly, then what sum will amount to INR 51,840 in 2 years at the rate of 40% per annum on compound interest?
Option 1: INR 25,000
Option 2: INR 15,000
Option 3: INR 20,000
Option 4: INR 30,000