Question

Khushnaz borrows a sum of ₹ 8000 for 2 years at SI and immediately lends out this money to another person at CI for the same period at the same rate. If she makes a profit of ₹ 96.80 on this transaction at the end of two years, calculate the rate of interest.

Answer 1

Given, Khushnaz borrows a sum of ₹ 8000 for 2 years at SI and immediately lends out this money to another person at CI for the same period at the same rate. She makes a profit of ₹ 96.80 on this transaction at the end of two years.

Simple interest = `(P xx R xx T)/100`, where P is the principal, R is the rate of interest and T is the time period

Compound interest = `P(1 + R/100)^T - 1`, where P is the principal, R is the rate of interest and T is the time period

According to the question:

`8000(1 + R/100)^2 - (8000 xx R xx 2)/100 = 96.80`

⇒ `[1 + R/50 + R^2/10000 - 1 - R/50] = 96.80/8000`

⇒ `R^2/10000 = 96.80/8000`

⇒ `R = sqrt(96.80/8000 xx 10000)`

⇒ `R = sqrt(121)`

⇒ `R = 11`

Hence, the rate of interest per annum is 11%.