The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Tk. 1. The sum is:

Question: The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Tk. 1. The sum is:

Solution:
Let the sum be Tk. x.

Compound interest = x{1 + (4/100)}² - x
= x{1 + (1/25)}² - x
= x(26/25)² - x
= (676x/625) - x
= (676x - 625x)/625
= 51x/625

Simple interest = (x × 4 × 2)/100
= 2x/25

ATQ,
(51x/625) - (2x/25) = 1
⇒ (51x - 50x)/625 = 1
∴ x = 625