Question : The simple interest on a certain sum of money for 2 years at 5% is Rs. 1600. The compound interest at the same rate after 3 years (interest compounded annually) is:
Option 1: Rs. 2520
Option 2: Rs. 2522
Option 3: Rs. 2555
Option 4: Rs. 2535
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Correct Answer: Rs. 2522
Solution :
Rate, $R$ = 5%
Time, $n$ = 2 years
Simple interest, SI = Rs. 1600
Let the principal be Rs. $P$.
Simple interest after 2 years = $\frac{PnR}{100}$
⇒ 1600 = $\frac{P × 2 × 5}{100}$
⇒ $P$ = Rs. 16000
When compounded annually, compound interest after $n$ years = $P[(1+\frac{R}{100})^{n} –1]$
Rate, $R$ = 5%
Time, $n$ = 3 years
So, the compound interest after 3 years = $16000[(1+\frac{5}{100})^{3} –1]$
= $16000 × [(\frac{21}{20})^3-1]$
= $16000× (\frac{1261}{8000})$
= Rs. 2522
Hence, the correct answer is Rs. 2522.
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