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
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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