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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