---
title: "Compounding semi-annually and monthly, 10% nominal"
subject: "Engineering Economics"
chapter: 2
key: "semester_6/engineering_economics:deposit-10000-semiannual-monthly"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/deposit-10000-semiannual-monthly
site: BCT Engineering
---

# Compounding semi-annually and monthly, 10% nominal

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

- Asked in: 2070 Magh, 2 marks
- Video: [Converting Nominal Interest Rates to Different Compounding Periods](https://www.youtube.com/watch?v=A2HLQIQBv64) — Study Force
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/engineering_economics/deposit-10000-semiannual-monthly
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-2

## Question

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?

## 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.

## Answer

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%).

## Check yourself

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

1. Which formula is used?
   A. F = P(1 + r)^m
   B. F = P(1 + r/N)^m
   C. F = P(1 + r/m)^(mN)
   D. F = P + P r N
   Answer: C. Rate per period r/m over mN periods. (Key point: Formula)

2. Semi-annual: rate and periods?
   A. 10% per period, 5 periods
   B. 2.5%, 20 periods
   C. 5%, 5 periods
   D. 5% per period, 10 periods, Rs 16,289
   Answer: D. 1.05^10 = 1.62889. (Key point: Semi-annual)

3. Which is larger and why?
   A. Monthly (Rs 16,453), because more frequent compounding gives a higher effective rate
   B. Semi-annual, as periods are longer
   C. Equal
   D. Semi-annual, higher rate per period
   Answer: A. Effective rate 10.47% vs 10.25%. (Key point: Monthly vs semi)

## Related in Engineering Economics

- [Deposit now to draw growing monthly amount](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Adeposit-now-growing-withdrawal) — 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
- [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 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×
- [Define equivalent worth and ROR; deposit to draw monthly](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Aequivalent-worth-ror-draw-monthly-10000) — 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

## Related in other subjects

- [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