---
title: "Nominal vs effective rate; quarterly rate from monthly"
subject: "Engineering Economics"
chapter: 2
key: "semester_6/engineering_economics:nominal-effective-monthly-1-quarterly"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/nominal-effective-monthly-1-quarterly
site: BCT Engineering
---

# Nominal vs effective rate; quarterly rate from monthly

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

- Asked in: 2065 Kartik, 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-monthly-1-quarterly
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-2

## Question

Differentiate between nominal interest rate and effective interest rate. If monthly interest rate is 1%, what will be the quarterly interest rate?

## Short answer

Nominal rate ignores compounding within a period; effective rate includes it. With 1% monthly, effective quarterly rate = (1.01)^3 - 1 = 3.0301% (nominal quarterly 3%).

## Answer

#### Nominal vs effective interest rate
| Point | Nominal rate | Effective rate |
|---|---|---|
| Definition | Stated rate for a year (or period), not counting compounding inside it | Actual rate for the period after compounding |
| Calculation | r = rate per sub-period × m | i = (1 + r/m)^m − 1 |
| Compounding | Ignored | Included |
| Value | Lower (or equal) | Higher (or equal) |
| Example | 12% per year, compounded monthly | 12.68% per year |
| Use in formulas | Not used directly | Used in factors once period matches payment period |

#### Quarterly rate from monthly rate
Monthly rate = 1%, and a quarter has 3 months.

- Nominal quarterly rate = 3 × 1% = 3%
- Effective quarterly rate i = (1 + 0.01)^3 − 1 = 1.030301 − 1 = **3.0301%**

**Answer: the quarterly interest rate is 3.03% (effective); the nominal quarterly rate is 3%.**

## Check yourself

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

1. What distinguishes the effective rate from the nominal rate?
   A. The effective rate ignores compounding
   B. The effective rate is always lower
   C. The effective rate includes compounding within the period
   D. The effective rate is the rate per sub-period times m
   Answer: C. Nominal = rate per sub-period x m, ignoring compounding; effective includes it and is higher or equal. (Key point: Nominal vs effective)

2. Which formula gives the effective rate per year for nominal r compounded m times?
   A. i = (1 + r/m)^m - 1
   B. i = r x m
   C. i = (1 + r)^m - 1
   D. i = r/m
   Answer: A. Effective rate i = (1 + r/m)^m - 1, e.g. 12% monthly compounding gives 12.68%. (Key point: Formula)

3. With 1% per month, what is the effective quarterly rate?
   A. 3%
   B. 3.0301%
   C. 3.3%
   D. 1.0301%
   Answer: B. (1.01)^3 - 1 = 0.030301, i.e. 3.0301%. (Key point: Quarterly rate)

4. What is the nominal quarterly rate from 1% per month?
   A. 3.03%
   B. 12%
   C. 4%
   D. 3%
   Answer: D. Nominal is just 3 x 1% = 3%, ignoring compounding. (Key point: Nominal quarterly)

## Related in Engineering Economics

- [Nominal vs effective; FW with monthly compounding](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Afw-monthly-compounding-annual-begin) — Engineering Economics, chapter 2, asked 2×
- [Nominal vs effective rate; simple vs compound deposit](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Anominal-effective-simple-compound-1000) — Engineering Economics, chapter 2
- [Nominal and effective rate for perpetual withdrawals](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Anominal-effective-perpetual-withdrawal-1000) — Engineering Economics, chapter 2
- [Monthly deposits with quarterly compounding, future amount](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Adeposit-quarterly-monthly-five-years) — Engineering Economics, chapter 2
- [Monthly deposits, quarterly compounding, balance at year 8](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Aequal-monthly-deposits-balance-8-years) — Engineering Economics, chapter 2
- [Nominal vs effective; FW with continuous compounding](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Afw-continuous-compounding-500) — Engineering Economics, chapter 2, asked 2×

## Related in other subjects

- [Conditional operator vs if-else; digit sum](https://www.bctengineer.com/question.md?key=semester_1%2Fcomputer_programming%3Aconditional-operator-vs-ifelse) — Computer Programming, chapter 5
- [Best installed capacity at 10% interest](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Abest-installed-capacity-10pct) — Hydro Power, chapter 3