---
title: "Simple vs compound interest; number of deposits"
subject: "Engineering Economics"
chapter: 2
key: "semester_6/engineering_economics:simple-vs-compound-deposits-20-lakh"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/simple-vs-compound-deposits-20-lakh
site: BCT Engineering
---

# Simple vs compound interest; number of deposits

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

- Asked in: 2069 Poush
- Video: [Simple vs. Compound Interest](https://www.youtube.com/watch?v=gyiiqUQgEeA) — Takota Asset Management
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/engineering_economics/simple-vs-compound-deposits-20-lakh
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-2

## Question

Differentiate between simple interest and compound interest. How many deposits of Rs. 50,000 each should be made per month so that the future amount will be Rs. 20,00,000 if the bank interest rate is 10% per year?

## Short answer

Simple interest is charged on principal only; compound interest on principal plus accumulated interest. To accumulate Rs 20,00,000 with Rs 50,000 monthly deposits at 10% nominal annual rate compounded monthly, about 35 deposits are needed (last may be slightly smaller).

## Answer

#### Simple vs compound interest
| Basis | Simple interest | Compound interest |
|---|---|---|
| Interest charged on | Original principal only | Principal plus interest already earned |
| Formula | I = P·i·n, F = P(1 + i·n) | F = P(1 + i)^n |
| Growth | Linear (straight line) | Exponential |
| Interest per period | Same every period | Increases every period |
| Use | Short-term loans, bills | Banks, long-term investment, engineering economy |
| Value after n > 1 | Smaller | Larger |

Example: Rs 1,000 at 10% for 3 years gives F = 1,300 (simple) and F = 1,331 (compound).

#### Number of deposits
Assumption: 10% per year is nominal, compounded monthly; deposits are made at the end of each month.

- Monthly i = 10% / 12 = 0.8333%
- F = A (F/A, i, n), so (F/A, 0.8333%, n) = F / A = 20,00,000 / 50,000 = 40
- [(1 + i)^n − 1] / i = 40
- (1 + i)^n = 1 + 40 × 0.008333 = 1.33333
- n = ln(1.33333) / ln(1.008333) = 0.28768 / 0.00830 = 34.67

Check: n = 34 gives F = 50,000 × 39.119 = Rs 1,955,940 (short); n = 35 gives F = 50,000 × 40.445 = Rs 2,022,239.

**Answer: about 35 monthly deposits of Rs 50,000 (34.67 ≈ 35; the last deposit can be slightly smaller).**

## Check yourself

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

1. Interest is charged on what in compound interest?
   A. Principal plus interest already earned
   B. Original principal only
   C. Interest only
   D. Final amount
   Answer: A. Compound interest grows exponentially. (Key point: Simple vs compound)

2. What equation gives n?
   A. n = F/A = 40
   B. (1+i)^n = 1 + (F/A) x i = 1.3333, i = 0.8333% per month
   C. (1+i)^n = 40
   D. n = F/(A i)
   Answer: B. Rearranging F = A[(1+i)^n - 1]/i. (Key point: Condition)

3. How many deposits?
   A. 34, which reaches the target
   B. 40
   C. About 35 (34.67 rounded up)
   D. 20
   Answer: C. n = 34 gives only Rs 1,955,940, short of 20 lakh. (Key point: n result)

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