Compound interest on a certain sum for 2 years at 10% per annum is Tk. 420. What would be the simple interest at the same rate and for the same time?

Question: Compound interest on a certain sum for 2 years at 10% per annum is Tk. 420. What would be the simple interest at the same rate and for the same time?

Solution:
Let, Principle = P
Compound Principle, C = P(1 + r)ⁿ
= P(1 + 10/100)²

ATQ,
C - P = 420
⇒ P(1 + 10/100)² - P = 420
⇒ P{(11/10)² - 1} = 420
⇒ P{(121/100) - 1} = 420
⇒ P(121- 100)/100 = 420
⇒ P(21/100) = 420
⇒ P = (420 × 100)/21
∴ P = 2000

Again,
I = Pnr
= 2000 × 2 × 10/100
= 400 tk.