Question

A sum of Rs $1000$ is invested at $12\%$ simple interest per year. Find the sum of all the interest generated every year for a period of $30$ years.

• A. Rs. 59400
• B. Rs. 52200
• C. Rs. 55800
• D. Rs. 3600

Answer 1

The correct option is C

Rs. 55800

We know that the formula to calculate simple interest is given by

Simple Interest = $\frac{P\times R\times T}{100}$

So, the interest at the end of the 1st year =Rs 1000 $\times$ 12 $\times$ $\frac{1}{100}$ = Rs 120

The interest at the end of the 2nd year =Rs 1000 $\times$12 $\times$ $\frac{2}{100}$= Rs 240

The interest at the end of the 3rd year =Rs 1000 $\times$12 $\times$ $\frac{3}{100}$ = Rs 360

Similarly, we can obtain the interest at the end of the 4th year, 5th year, and so on.

So, the interest (in Rs) at the end of the 1st, 2nd, 3rd, . . . years, respectively are 120, 240, 360, . . .

It is an AP as the difference between the consecutive terms in the list is 120, i.e.

d = 120. Also, a = 120.

So, to find sum of the interest at the end of 30 years, we shall find $S_{30}$.

Now,

$S_{30}$ = $\frac{n}{2}(2a+(n-1\left)d\right)$

$\Rightarrow S_{30}=15(240+29\times 120)=55800$

So, the interest at the end of 30 years will be Rs 55800.