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 annum, when the interest is compounded yearly. The rate of interest is:
Option 1: 12%
Option 2: 15%
Option 3: 20%
Option 4: 8%
Correct Answer: 12%
Solution :
Let $P$ be the principal sum and $R$ be the interest rate.
Total amount after $n$ years, compounded annually = $P(1+\frac{R}{100})^n$
Total amount after 4 years = INR 7,562
$P(1+\frac{R}{100})^4=7562$ -------------(i)
Total amount after 5 years = INR 8,469.44
$P(1+\frac{R}{100})^5=8469.44$ -------------(ii)
Dividing (ii) by (i),
$1+\frac{R}{100} = \frac{8469.44}{7562}$
⇒ $1+\frac{R}{100} = 1.12$
⇒ $\frac{R}{100} = 0.12$
⇒ $R=0.12 × 100=12$%
Hence, the correct answer is 12%.
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