A man invests ₹8,000 in a finance company that provides 24% annual compound…
2023
A man invests ₹8,000 in a finance company that provides 24% annual compound interest, compounded monthly. Compute the compound interest on the invested amount for 3 months.
Answer: B. ₹489.66 — ConceptFor monthly compounding, first convert the annual nominal rate to a monthly rate. If the principal is P, the monthly rate is i, and the number of…
- A.
₹555.66
- B.
₹489.66
- C.
₹589.66
- D.
₹689.66
Show answer & explanation
Correct answer: B
Concept
For monthly compounding, first convert the annual nominal rate to a monthly rate.
If the principal is P, the monthly rate is i, and the number of months is m, then the accumulated amount is A = P(1 + i)m and the compound interest is A − P.
Application
The monthly rate is i = 24% ÷ 12 = 2% = 0.02.
For three months, m = 3, so A = 8,000(1 + 0.02)3.
Calculate the growth factor: (1.02)3 = 1.061208.
Thus A = 8,000 × 1.061208 = ₹8,489.664.
Compound interest = A − P = ₹8,489.664 − ₹8,000 = ₹489.664, which rounds to ₹489.66 to two decimal places.
Cross-check
Month-by-month, the balances are ₹8,160 after month 1, ₹8,323.20 after month 2, and ₹8,489.664 after month 3. The increase over ₹8,000 is ₹489.664, confirming the result.
Therefore, the compound interest for three months is ₹489.66.