Robi invested Tk. ‘x’ in a scheme offering 15% p.a. simple interest for three years while Shami invested same amount in another scheme offering 10% p.a. compound interest for three years, compounded annually. Find the value of ‘x’ if the difference between the interests earned by them after three is Tk. 1428.

Question: Robi invested Tk. ‘x’ in a scheme offering 15% p.a. simple interest for three years while Shami invested same amount in another scheme offering 10% p.a. compound interest for three years, compounded annually. Find the value of ‘x’ if the difference between the interests earned by them after three is Tk. 1428.

Solution:
Robi invested Tk. ‘x’ in a scheme offering 15% p.a. simple interest for three years
∴ Simple interest = x × 3 × (15/100) = 9x/20 = 0.45x

Shami invested Tk. x in another scheme offering 10% p.a. compound interest for three years
∴ Compound interest = x(1 + 10/100)³ - x
= x × 1.1 × 1.1 × 1.1 - x
= 1.331x - x
= 0.331x

ATQ,
0.45x - 0.331x = 1428
⇒ 0.119x = 1428
⇒ x = 1428/0.119
∴ x = 12000