Question : Rajeev invested Rs. 3,000 for 2 years at compound interest (compounded annually) in a company that paid him interest of Rs.1,320. What will be the annual rate of interest at which Rajeev invested his money?
Option 1: 30 percent
Option 2: 24 percent
Option 3: 16 percent
Option 4: 20 percent
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Correct Answer: 20 percent
Solution :
Given, Principal ($P$) = Rs. 3000
Compound Interest ($CI$) = Rs. 1320
Time (t) = 2 years
We know, $CI = P(1 + \frac{r}{100})^t - P$
⇒ $1320 = 3000(1+\frac{r}{100})^2 - 3000$
⇒ $1320+3000 = 3000(1+\frac{r}{100})^2$
⇒ $\frac{4320}{3000}=(1+\frac{r}{100})^2$
⇒ $\sqrt{1.44}=(1+\frac{r}{100})$
⇒ $1.2 = (1+\frac{r}{100})$
⇒ $1.2-1 = \frac{r}{100}$
⇒ $r = 0.2\times 100 = 20\%$
Hence, the correct answer is 20 percent.
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