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
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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