---
title: "Nominal vs effective rate; simple vs compound deposit"
subject: "Engineering Economics"
chapter: 2
key: "semester_6/engineering_economics:nominal-effective-simple-compound-1000"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/nominal-effective-simple-compound-1000
site: BCT Engineering
---

# Nominal vs effective rate; simple vs compound deposit

Engineering Economics · Chapter 2: Interest and Time Value of Money

- Asked in: 2072 Asoj, 2+4 marks
- Video: [Nominal and Effective Interest Rates - Engineering Economics Lightboard](https://www.youtube.com/watch?v=aT1n_bbQQbM) — Engineering Economics Guy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/engineering_economics/nominal-effective-simple-compound-1000
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-2

## Question

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?

## 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.

## Answer

#### 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.**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is the effective rate formula?
   A. i = (1 + r/m)^m - 1
   B. i = r/m
   C. i = r x m
   D. i = (1 + r)^m
   Answer: A. Effective rate accounts for compounding m times a year. (Key point: Effective rate)

2. What is the amount for Rs 1,000 at 4% simple for 10 years?
   A. Rs 1,480.24
   B. Rs 1,400
   C. Rs 1,040
   D. Rs 1,004
   Answer: B. I = 1,000 x 0.04 x 10 = 400. (Key point: Simple interest)

3. What is the compound amount?
   A. Rs 1,400
   B. Rs 1,400.24
   C. Rs 1,480.24
   D. Rs 1,040
   Answer: C. F = 1,000 (1.04)^10. (Key point: Compound)

4. How is interest on interest found?
   A. Compound interest alone
   B. Simple interest minus 400
   C. 4% of 1,000
   D. Compound interest minus simple interest = Rs 80.24
   Answer: D. 480.24 - 400 = 80.24. (Key point: Interest on interest)

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