Question

A sum of Rs 1000 is invested at 8$\%$ simple interest per year. Calculate the interest for first three years and find the sum of the interest for first three years.

• A. Rs.80, Rs.120, Rs.240 Sum = Rs.440
• B. Rs.80, Rs.160, Rs.240 ; Sum = Rs.480
• C. Rs.80, Rs.150, Rs.220 ; Sum = Rs.450
• D. Rs.120, Rs.240, Rs.360 ; Sum = Rs.720

Answer 1

The correct option is B

Rs.80, Rs.160, Rs.240 ; Sum = Rs.480

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$8$\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

So, the interest (in Rs) at the end of the 1st, 2nd and 3rd years, respectively are 80, 160, and 240.

Sum of the first three interest = 80 + 160 + 240 = Rs. 480

Or

These three terms are AP

a = 80, d = 80.

Sum,

$S_3$ = $\frac{3}{2}$ ( 2 $\times$ 20 + (3 - 1) 80 )

= Rs. 480

So, the interest at the end of 3 years will be Rs 480.