---
title: "Capitalized worth; deposit for perpetual withdrawals"
subject: "Engineering Economics"
chapter: 2
key: "semester_6/engineering_economics:capitalized-worth-3000-monthly-20000-50000"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/capitalized-worth-3000-monthly-20000-50000
site: BCT Engineering
---

# Capitalized worth; deposit for perpetual withdrawals

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

- Asked in: 2067 Mangsir, 2+6 marks
- Video: [Capitalized Value - Present Value of a Perpetuity (live class recording)](https://www.youtube.com/watch?v=5oOR7z6WnJg) — 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/capitalized-worth-3000-monthly-20000-50000
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-2

## Question

Define capitalized worth. How much money should Mr X deposit now in a bank which gives 12% interest annually, so that he can draw Rs 3000 per month plus Rs. 20,000 annually and Rs. 50,000 in every five years for infinite period?

## Short answer

Capitalized worth is the present sum that yields a perpetual series of payments. Using 12% nominal compounded monthly (effective annual 12.683%), required deposit = 3000/0.01 + 20000/0.12683 + 50000(A/F,12.683%,5)/0.12683 ≈ Rs 5,18,920.

## Answer

#### Capitalized worth
Capitalized worth (CW) is the present worth of a series of cash flows that continues forever (infinite life). For a uniform perpetual amount A it is CW = A / i. For a perpetual series that repeats every k years, convert each payment to an equivalent end-of-year amount first, then divide by i. It is used for bridges, dams, endowments and scholarships.

#### Numerical
Assumption: 12% per year is the nominal rate compounded monthly, so monthly i = 1% and effective annual i = (1.01)^12 − 1 = 12.683%.

```text
 Monthly : 3,000 every month, forever
 Annual  : 20,000 every year, forever
 5-yearly: 50,000 at years 5, 10, 15, ... forever
```
**1. Monthly Rs 3,000**
P₁ = 3,000 / 0.01 = Rs 300,000

**2. Annual Rs 20,000**
P₂ = 20,000 / 0.12683 = Rs 157,698

**3. Rs 50,000 every 5 years**
- Equivalent annual amount A = 50,000 (A/F, 12.683%, 5) = 50,000 × 0.15529 = Rs 7,764.51
- P₃ = 7,764.51 / 0.12683 = Rs 61,222

**Total deposit**
P = P₁ + P₂ + P₃ = 300,000 + 157,698 + 61,222

**Answer: Mr X should deposit about Rs 518,920 (≈ Rs 5.19 lakh).**

(If 12% is taken as the effective annual rate, the monthly rate is 0.9489% and the total becomes about Rs 548,417.)

## Check yourself

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

1. CW of a perpetual uniform amount?
   A. A x i
   B. A(1+i)
   C. A/n
   D. A/i
   Answer: D. Present worth of infinite series. (Key point: Capitalized worth)

2. How is Rs 50,000 every 5 years handled?
   A. Convert to annual equivalent with (A/F,i,5), then divide by i
   B. Divide 50,000 by 12%
   C. Multiply by 5
   D. Divide by 0.01
   Answer: A. A = 50,000 x 0.15529 = 7,764.51, P3 = 7,764.51/0.12683. (Key point: Every five years)

3. P1 for Rs 3,000/month?
   A. Rs 25,000
   B. Rs 300,000
   C. Rs 157,698
   D. Rs 36,000
   Answer: B. 3,000/0.01. (Key point: Monthly part)

4. Total deposit?
   A. Rs 3 lakh
   B. Rs 1.57 lakh
   C. About Rs 5.19 lakh
   D. Rs 6.12 lakh
   Answer: C. 300,000 + 157,698 + 61,222. (Key point: Total)

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