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
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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