The difference between compound interest and simple interest on a certain sum of money for 2 years at 5% per annum, compounded annually, is Tk. 25. What is the principal (sum)?

Question: The difference between compound interest and simple interest on a certain sum of money for 2 years at 5% per annum, compounded annually, is Tk. 25. What is the principal (sum)?

Solution:
Let,
The principal = P

So the simple interest(SI) = Prn
= P × 5% × 2
= P × 5/100 × 2
= P/10

So the compound interest(CI) = P(1 +r)ⁿ - P
= P{(1 + 5/100)² - 1}
= P{(21/20)² - 1}
= P{441/400 - 1}
= P{(441 - 400)/400}
= 41P/400

ATQ,
(41P/400) - (P/10) = 25
⇒ (41P - 40P)/400 = 25
⇒ P/400 = 25
⇒ P = 25 × 400
∴ P = 10000