A sum of money lent at compound interest for 2 years at 20% per annum would…
2025
A sum of money lent at compound interest for 2 years at 20% per annum would fetch ₹482 more if the interest was payable half yearly than if it was payable annually. Find the sum of money lent.
- A.
₹15,000
- B.
₹13,000
- C.
₹18,000
- D.
₹20,000
Attempted by 3 students.
Show answer & explanation
Correct answer: D
Let the sum of money lent be P.
Case 1: Interest payable annually. Rate = 20%, Time = 2 years.
Amount = P(1 + 20/100)^2 = P(1.2)^2 = 1.44P
Case 2: Interest payable half-yearly. Rate = 10% per half-year, Time = 4 periods.
Amount = P(1 + 10/100)^4 = P(1.1)^4 = 1.4641P
Difference in amounts = 1.4641P - 1.44P = 0.0241P
Given difference = ₹482, so 0.0241P = 482
P = 482 / 0.0241 = ₹20,000