Question : A sum amounts to INR 7,562 in 4 years and to INR 8,469.44 in 5 years, at a certain rate per cent per annum when the interest is compounded yearly. If INR 10,000 at the same rate of interest is borrowed for two years, then what will be the compound interest (in INR)?
Option 1: 2,544
Option 2: 1,736
Option 3: 2,764
Option 4: 1,965
Correct Answer: 2,544
Solution :
Let P be the principal.
We know, $\text{Total Amount}=\text{Principal}×(1+\frac{\text{Rate}}{100})^{\text{Time}}$
$\text{P}(1 +\frac{r}{100})^4$ = 7562 -----------------(1)
$\text{P}(1 +\frac{r}{100})^5$ = 8469.44 -------------(2)
Dividing (2) by (1) we get,
$(1 +\frac{r}{100}) = \frac{846944}{756200}$
$⇒\frac{r}{100} = 1.12 - 1$
$\therefore r = 12$
Compound Interest $=10,000 × [(1 + \frac{12}{100})^2 – 1]= 10000 × 0.2544 =$ INR $2,544$
Hence, the correct answer is INR 2,544.
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