Question

A sum of Rs 1000 is invested at 8% simple interest per year. Calculate the interest at the end of each year. Do these interests form an AP? If so, find the interest at the end of 30 years making use of this fact.

Answer 1

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

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

So, the interest at the end of the 1st year =Rs 1000 $\times$8 $\times$ $\frac{1}{100}$ = Rs 80

The interest at the end of the 2nd year =Rs 1000 $\times$8 $\times$ $\frac{2}{100}$ = Rs 160

The interest at the end of the 3rd year =Rs 1000 $\times$8 $\times$ $\frac{3}{100}$ = Rs 240

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

So, the interest (in Rs) at the end of the $1^{st}$, $2^{nd}$, $3^{rd}$, . . . years, respectively are

80, 160, 240, . . .

It is an AP as the difference between the consecutive terms in the list is 80, i.e.

d = 80. Also, a = 80.

So, to find the interest at the end of 30 years, we shall find $a_{3}0$.

Now, $a_{3}0$= a + (30 – 1) d = 80 + 29 $\times$ 80 = 2400

So, the interest at the end of 30 years will be Rs 2400.