Compound Interest on Loan at “2.5 paise per rupee per annum” — 3-year horizon: Vijay obtains a loan of ₹ 64000. The rate is 2.5 paise per rupee per annum (i.e., 2.5% p.a.) compounded yearly. Find the compound interest payable after 3 years.
Aptitude
Compound Interest
Difficulty: Easy
Choose an option
Answer
Correct Answer: Rs. 4921
Explanation
Introduction / Context:Rates sometimes appear as “paise per rupee per annum.” Since 100 paise = 1 rupee, 2.5 paise per rupee equals 2.5/100 = 0.025 = 2.5% per annum. Use standard compound interest with annual compounding to compute the total interest for the given horizon.
Given Data / Assumptions:
- Principal P = ₹ 64000
- Annual rate r = 2.5% = 0.025
- Time t = 3 years; annual compounding
Concept / Approach:Amount after 3 years: A = P(1 + r)^3. The compound interest (CI) equals A − P = P[(1 + r)^3 − 1]. Plug in r = 0.025 and compute the factor precisely.
Step-by-Step Solution:
(1.025)^3 = 1.076890625.Interest factor = 1.076890625 − 1 = 0.076890625.CI = 64000 * 0.076890625 = ₹ 4921 (exact to the rupee).Verification / Alternative check:
Compute A = 64000 * 1.076890625 = ₹ 68921.00; A − P = 4921.00.Why Other Options Are Wrong:
- ₹ 4920 is rounding-down; ₹ 5020, ₹ 4821, ₹ 5000 do not match exact compounding.
Common Pitfalls:
- Interpreting 2.5 paise per rupee as 2.5% points incorrectly.
Final Answer:Rs. 4921.