Question : A sum of money, when invested at the rate of 6.25% simple interest per annum, amounts to $\frac{11}{8}$ times itself in $n$ years. What is the value of $n$?
Option 1: 6
Option 2: 8
Option 3: 5
Option 4: 7
Correct Answer: 6
Solution :
Given:
Rate $(r)$ = 6.25% per annum
Time $(t)$ = $n$ years
Let the principal be $x$.
Amount $=\frac{11}{8}\times $ Principal $= \frac{11x}{8}$
Simple interest = Amount – Principal $= \frac{11x}{8} - x= \frac{3x}{8}$
We know, Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$
According to the question,
$\frac{3x}{8} = \frac{x\times 6.25\times n}{100}$
$\Rightarrow \frac{300}{8} = 6.25n$
$\Rightarrow n= \frac{300}{8\times 6.25}$
$\therefore n= 6$ years
Hence, the correct answer is 6 years.
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