Question

The difference between compound interest and simple interest on an amount of 15000 for 2 years is rs96. What is the rate of interest per annum?

Answer 1

Let the rate of interest per annum = r.
Simple Interest SI = Prt where P = Principal = 15000; and t = time in years = 2 years
Therefore SI = 15000r(2) = 30000r.
Compound interest amount A = P(1+r)${}^t$ where P= Principal = 15000, r = annual rate of interest and t is time in years = 2 years as before.
Therefore A = 15000(1+r)${}^2$
Compound interrest CI= Amount after 2 years - Principal = A-P = 15000(1+r)${}^2$ -15000 =15000((1+r)${}^2$-1) = 15000(1+2r+$r^2$ -1)=15000(2r+$r^2$)
We are given that the difference between compound interest and simple interest on an amount of 15000 for 2 years is Rs 96.
It means CI - SI = 96 or
15000(2r+$r^2$)-30000r = 96
30000r+15000$r^2$ -30000r = 96
15000$r^2$ = 96
$r^2$= 96/15000= 0.0064
r = $\sqrt{0.0064}$ = 0.08 or 8%
Answer: 8%