---
title: "Nominal and effective rate for perpetual withdrawals"
subject: "Engineering Economics"
chapter: 2
key: "semester_6/engineering_economics:nominal-effective-perpetual-withdrawal-1000"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/nominal-effective-perpetual-withdrawal-1000
site: BCT Engineering
---

# Nominal and effective rate for perpetual withdrawals

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

- Asked in: 2068 Jestha, 6 marks
- Video: [Effective annual interest rate (EAR)](https://www.youtube.com/watch?v=L39WeJRWvvw) — The Finance Storyteller
- 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-perpetual-withdrawal-1000
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-2

## Question

Differentiate between nominal and effective interest. Calculate both nominal and effective annual interest if you deposit now Rs 1,00,000 and you can draw Rs 1000 per month forever.

## Short answer

Nominal rate ignores intra-year compounding; effective rate includes it. For a deposit of Rs 1,00,000 yielding Rs 1,000 per month forever: nominal annual rate = 12%, effective annual rate = 12.68%.

## Answer

#### Nominal vs effective interest
| Point | Nominal rate (r) | Effective rate (i) |
|---|---|---|
| Meaning | Stated yearly rate, ignoring compounding within the year | Actual yearly rate including compounding |
| Compounding | Not reflected | Fully reflected |
| Formula | r = m × (rate per period) | i = (1 + r/m)^m − 1 |
| Example | 12% compounded monthly | 12.68% per year |
| Relation | r ≤ i (equal only when m = 1) | i ≥ r |

#### Numerical
Withdrawals continue forever, so the deposit works as a perpetuity: P = A / i.

```text
 P = 1,00,000 at t = 0;   1000 drawn at the end of every month, forever
```
- Interest per month i = A / P = 1,000 / 1,00,000 = 0.01 = 1% per month
- Nominal annual rate r = 12 × 1% = **12% per year** (compounded monthly)
- Effective annual rate i = (1 + 0.01)^12 − 1 = 1.12683 − 1 = **12.68% per year**

**Answer: nominal = 12% per year; effective = 12.68% per year.**

## Check yourself

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

1. Which formula is used for forever withdrawals?
   A. P = A x i
   B. P = A(F/A,i,n)
   C. P = A/n
   D. P = A/i
   Answer: D. Interest per period equals the withdrawal. (Key point: Perpetuity)

2. Monthly rate for Rs 1,000 from Rs 1,00,000?
   A. 1% per month
   B. 12%
   C. 0.1%
   D. 10%
   Answer: A. 1,000/100,000. (Key point: Monthly rate)

3. Nominal annual rate?
   A. 12.68%
   B. 12% (12 x 1%)
   C. 1%
   D. 11.4%
   Answer: B. Nominal = m x period rate. (Key point: Nominal)

4. Effective annual rate?
   A. 12%
   B. 13%
   C. (1.01)^12 - 1 = 12.68%
   D. 10.68%
   Answer: C. Compounding makes effective exceed nominal. (Key point: Effective)

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