A person borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6% p.a compound interest for 2 years. Find his total gain in the transaction.

Question: A person borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6% p.a compound interest for 2 years. Find his total gain in the transaction.

Solution:
Given,
P = Tk. 5000
n = 2 years
r = 4% = 4/100 = 1/25

So the simple interest = 5000 × (1/25) × 2
= Tk. 400

Again,
compound interest rate r = 6% = 6/100 = 3/50

So,
The compound interest = P(1 + r)ⁿ - P
= 5000(1 + 3/50)² - 5000
= {5000 × (53/50)²} - 5000
= (5000 × 2809/2500) - 5000
= 5618 - 5000
= 618

So the total gain in the transaction = (618 - 400)
= Tk. 218