Question : The compound interest (compounding annually) on a certain sum at the rate of 8% per annum for two years is INR 6,656. What would be the simple interest on the same sum at the same rate of interest for two years?
Option 1: INR 5,600
Option 2: INR 6,224
Option 3: INR 6,400
Option 4: INR 6,336
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Correct Answer: INR 6,400
Solution : Given: The compound interest (compounding annually) on a certain sum at the rate of 8% per annum for two years is INR 6,656. We know the formulas, $A=P\times [1+\frac{R}{100}]^T$ $SI=\frac{P\times R\times T}{100}$ $A=SI+P$ $A=CI+P$ where $A$, $SI$, $CI$, $P$, $R$ and $T$ are the amount, simple interest, compound interest, principal, rate, and time respectively. According to the question, $CI+P=P\times [1+\frac{R}{100}]^T$ ⇒ $6656+P=P\times [1+\frac{8}{100}]^2$ ⇒ $6656+P=P\times (1.08)^2$ ⇒ $1.1664P –P=6656$ ⇒ $P=\frac{6656}{0.1664}$ ⇒ $P=$ INR 40,000 The simple interest on the same sum at the same rate of interest for two years $=\frac{40000\times8\times 2}{100}=$ INR 6,400 Hence, the correct answer is INR 6,400.
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