Question : A sum invested at a certain rate of interest per annum, compounded annually, amounts to INR 14,400 in 2 years and to INR 25,920 in 4 years. What is the sum invested?
Option 1: INR 8,200
Option 2: INR 7,500
Option 3: INR 8,500
Option 4: INR 8,000
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Correct Answer: INR 8,000
Solution : Given, A sum invested at a certain rate of interest per annum, compounded annually, amounts to INR 14,400 in 2 years and to INR 25,920 in 4 years. We know, Amount after $n$ years = $P(1+\frac{r}{100})^n$, where $P$ is the principal amount and $r$ is the interest rate per annum. After 2 years, $14400=P(1+\frac{r}{100})^2$ ⇒ $\frac{14400}{P}=(1+\frac{r}{100})^2$ After 4 years, $25290=P(1+\frac{r}{100})^4$ ⇒ $25920=P(\frac{14400}{P})^2$ ⇒ $P=\frac{14400×14400}{25920}$ ⇒ $P=8000$ Hence, the correct answer is INR 8000.
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