If the simple interest on a sum of money for 2 years at 5% per annum is Rs.…
2025
If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same at the same rate and for the same time?
Answer: A. Rs. 51.25 — Concept: Simple interest (SI) is calculated only on the original principal each year: SI = (P × R × T) / 100. Compound interest (CI) is calculated on the…
- A.
Rs. 51.25
- B.
Rs. 52
- C.
Rs. 54.25
- D.
Rs. 60
Attempted by 2 students.
Show answer & explanation
Correct answer: A
Concept: Simple interest (SI) is calculated only on the original principal each year: SI = (P × R × T) / 100. Compound interest (CI) is calculated on the amount that keeps including previously earned interest: Amount A = P(1 + R/100)T, and CI = A − P. Over the same principal, rate and time, CI is always slightly higher than SI, because interest itself starts earning interest.
Application:
Recover the principal from the given simple interest: SI = (P × R × T) / 100, so 50 = (P × 5 × 2) / 100, which gives P = Rs. 500.
Compound this principal for 2 years at 5% per annum: A = 500 × (1 + 5/100)2 = 500 × 1.1025 = Rs. 551.25.
Subtract the principal from the amount to get the compound interest: CI = 551.25 − 500 = Rs. 51.25.
Cross-check: Use the standard two-year shortcut: CI (2 years) = SI (2 years) + [SI (1 year) × R / 100]. Here SI for 1 year = 25, so the extra amount = 25 × 5 / 100 = 1.25, giving CI = 50 + 1.25 = Rs. 51.25 — the same result, confirming the answer independently.