- 2070 Magh · 2 marks
Compounding semi-annually and monthly, 10% nominal
Short answer
For semi-annual compounding: F = 10000 × (1.05)^10 = Rs 16,289. For monthly: F = 10000 × (1 + 0.10/12)^60 = Rs 16,453. More frequent compounding gives a slightly higher amount.
If you deposit Rs. 10000 in a saving account now which gives 10% nominal interest rate, what will be the amount after 5 years if interest is compounded (i) semi-annually (ii) monthly?
Use F = P (1 + r/m)^(mN), with P = Rs 10,000, nominal r = 10% per year, N = 5 years.
(i) Compounded semi-annually
m = 2, rate per period = 5%, periods = 10 F = 10,000 (F/P, 5%, 10) = 10,000 × (1.05)¹⁰ = 10,000 × 1.62889 = Rs 16,289
(ii) Compounded monthly
m = 12, rate per period = 10/12 = 0.8333%, periods = 60 F = 10,000 (1.008333)⁶⁰ = 10,000 × 1.64531 = Rs 16,453
Answer: (i) Rs 16,289; (ii) Rs 16,453. More frequent compounding gives a slightly higher amount (effective rate 10.25% vs 10.47%).
✓ Answer checked by Claude Opus 5.5 (high effort)
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