Question

Arun borrows ₹ 24,000 from Bryan at SI for 2 years at 5% p.a. and immediately lends out this money to Chand for 2 years at 5% p.a. compounded annually. What is Arun’s gain in this transaction?

Answer 1

Given, Arun borrows ₹ 24000 from Bryan at simple interest for 2 years at 5% per annum.

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

∴ Simple interest = `₹ ((24000 xx 2 xx 5)/100)` = ₹ 2400

Given, Arun borrows ₹ 24000 from Bryan at simple interest for 2 years at 5% per annum and immediately lends out this money to for 2 years at 5% p.a. compounded annually.

Compound interest = `P[(1 + r/100)^t - 1]`

∴ Compound interest = `24000[(1 + 5/100)^2 - 1]`

= `24000[(1 + 1/20)^2 - 1]`

= `24000[(21/20)^2 - 1]`

= `24000[441/400 - 1]`

= `24000[(441 - 400)/400]`

= `24000 xx 41/400`

= 2460

Arun’s gain = Compound interest – Simple interest

= ₹ (2460 – 2400)

= ₹ 60

Hence, Arun’s gain in this transaction is ₹ 60.