---
title: "Deposit for infinite bimonthly withdrawals"
subject: "Engineering Economics"
chapter: 2
key: "semester_6/engineering_economics:deposit-bimonthly-5000-infinite"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/deposit-bimonthly-5000-infinite
site: BCT Engineering
---

# Deposit for infinite bimonthly withdrawals

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

- Asked in: 2066 Magh, 6 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/engineering_economics/deposit-bimonthly-5000-infinite
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-2

## Question

How much money should Mr Ram deposit now in a bank so that he and his successor can draw Rs 5000 bimonthly for infinite period? Interest rate is 12% per year.

## Short answer

With 12% nominal annual rate, the two-monthly interest rate is 2%. Capitalized worth = 5000/0.02 = Rs 2,50,000.

## Answer

Assumption: "bimonthly" means once every two months, so there are 6 withdrawals per year. 12% per year is the nominal rate compounded every two months.

```text
 P = ?     withdrawals of 5,000 at months 2, 4, 6, 8, ... forever
```
- Interest per two-month period i = 12% / 6 = 2% = 0.02
- Withdrawal per period A = Rs 5,000
- For an infinite series, P = A / i (capitalized worth)
- P = 5,000 / 0.02 = Rs 2,50,000

The deposit is never used up because each period's interest (2% of 2,50,000 = Rs 5,000) is exactly the amount drawn, so the principal stays intact for the successors.

**Answer: Rs 2,50,000 should be deposited now.**

(If the withdrawal were twice a month, i = 0.5% per half-month and P = 5,000/0.005 = Rs 10,00,000.)

## Check yourself

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

1. Interest per two-month period?
   A. 12%/6 = 2%
   B. 12%
   C. 1%
   D. 0.5%
   Answer: A. Six periods in a year. (Key point: Period rate)

2. Deposit needed?
   A. Rs 10,00,000
   B. Rs 2,50,000 (5,000/0.02)
   C. Rs 5,000
   D. Rs 41,667
   Answer: B. P = A/i. (Key point: Deposit)

3. Why does the principal stay intact?
   A. Withdrawals are tiny
   B. Extra deposits are made
   C. Interest each period (2% of 2,50,000 = Rs 5,000) equals the withdrawal
   D. Rate rises
   Answer: C. The interest is fully drawn. (Key point: Why principal remains)

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