Question : If Rs. 2,500 becomes Rs. 2,970.25 in 2 years at compound interest compounded annually, what is the yearly rate of interest (in %)?
Option 1: 7
Option 2: 9
Option 3: 11
Option 4: 13
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Correct Answer: 9
Solution : Principal amount, P = Rs. 2,500 Term, n = 2 years Total amount A = Rs. 2,970.25 Let the rate be $R$. Total amount after 2 years A = $P(1+\frac{R}{100})^{2}$ ⇒ Rs. 2,970.25 = Rs. 2,500$(1+\frac{R}{100})^{2}$ ⇒ $(1+\frac{R}{100})^{2}$ = $\frac{2970.25}{2500}$ ⇒ $(1+\frac{R}{100})$ = $\sqrt{1.1881}$ ⇒ $1+\frac{R}{100}$ = 1.09 ⇒ R = 0.09 × 100 = 9% Hence, the correct answer is 9.
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