Question : If the difference between the compound interest and simple interest at 17%; on a sum of money for 2 years (compounded annually) is INR 433.50, then the compound interest (in INR) is:
Option 1: 2,735.50
Option 2: 2,500
Option 3: 5,100
Option 4: 5,533.50
Correct Answer: 5,533.50
Solution :
Given: Difference = INR 433.50
Rate = 17%
Time = 2 years
We know that,
$D=P(\frac{r}{100})^2$, where $D$ = Difference between CI and SI, $P$ = Principal, $r$ = Rate of interest
⇒ $433.50=P(\frac{17}{100})^2$
⇒ $433.50=P\times\frac{17}{100}\times\frac{17}{100}$
⇒ $P=15000$
Now, $CI= P((1+\frac{R}{100})^{T}-1)$
$= 15000((1+\frac{17}{100})^{2}-1)$
$= 15000((\frac{117}{100})^{2}-1)$
$= 15000(\frac{117}{100}\times\frac{117}{100}-1)$
$= 15000(\frac{13689}{10000}-1)$
$= 15000\times\frac{3689}{10000}$
$=5533.50$
Hence, the correct answer is INR 5533.50.
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