Question : The compound interest of Rs. 30,000 at 7% per annum for a certain time is Rs. 4,347. The time is:
Option 1: 3 years
Option 2: 4 years
Option 3: 2 years
Option 4: 2.5 years
Correct Answer: 2 years
Solution :
Sum, $P$ = Rs. 30,000
Rate, $R$ = 7%
Compound Interest = Rs. 4,347
Let $n$ be the time.
When compounded annually, Compound interest after n years = $P[(1+\frac{R}{100})^{n}–1]$, where $P$ is principal, $R$ is the rate of interest per annum compounded annually.
So, 4347 = 30000$[(1+\frac{7}{100})^{n}–1]$
$⇒1.07^n = \frac{4347}{30000}+1 = 1.1449$
$⇒1.07^n = 1.07^2$
$\therefore n$ = 2
Hence, the correct answer is 2 years.
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