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Nominal vs effective rate; simple vs compound deposit

Short answer

Nominal rate is stated rate; effective rate includes compounding effect. Simple interest yields Rs 1,400. Compound interest yields Rs 1,480.24. Interest on interest = Rs 80.24.

What is the difference between nominal and effective interest rate? You deposit Rs. 1000 in your bank account. If the bank pays 4% simple interest, how much will you accumulate in your account after 10 years? What if the bank pays compound interest? How much of your earnings will be interest on interest?

Nominal and effective interest rate

  • Nominal rate (r) is the stated annual rate, not counting compounding within the year, e.g. 12% per year compounded monthly.
  • Effective rate (i) is the actual annual rate after compounding within the year: i = (1 + r/m)ᵐ − 1, where m is the number of compounding periods per year. For 12% compounded monthly, i = (1.01)¹² − 1 = 12.68%.
  • Nominal = effective only when compounding is annual. Effective rate is always at least the nominal rate.

Simple interest, 4% for 10 years

Interest = P i n = 1,000 × 0.04 × 10 = Rs 400 F = 1,000 + 400 = Rs 1,400

Compound interest, 4% for 10 years

F = P (1 + i)ⁿ = 1,000 (F/P, 4%, 10) = 1,000 × 1.48024 = Rs 1,480.24 Total interest = Rs 480.24

Interest on interest

Interest on interest = compound interest − simple interest = 480.24 − 400 = Rs 80.24

Answer: Simple interest gives Rs 1,400; compound interest gives Rs 1,480.24; interest on interest is Rs 80.24.

✓ Answer checked by Claude Opus 5.5 (high effort)

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