Question

The difference between compound interest and simple interest on
15,000 for 2 years is 96. What is the rate of interest per annum? ..
with cancellation​

Answer 1

Step-by-step explanation:

let the rate of percent = R %

amount after 2 years on 15000 when interest is compound annually .

P ( 1 + r / 100 ) ^ T = 15000( 1 + R /100 )T

compound interest =

15000( 1 + R/ 100 )^ 2 - 15000

simple interest = P × R × T / 100

= 15000 × R × 2 / 100= 300R

Difference between compound interest and simple interest = rs. 96

15000 {( 1+ R / 100) ^2 - 1 }- 300R = rs 96

15000{ 1 + R ^ 2 / 10000+ 2R/ 100 - 1) - 300R = 96

15000 ( R ^ 2 / 10000+ 2R / 100) - 300R = 96

300R - 300 R + 15 R ^ 2 /10= 96

15 R ^ 2 /10 = 96

3 / 2 r ^ 2= 96

r ^ 2 = 96 × 2 / 3

r ^ 2 = 64

r = 8 %