---
title: "Capitalized worth and infinite-period deposit"
subject: "Engineering Economics"
chapter: 2
key: "semester_6/engineering_economics:capitalized-worth-monthly-yearly-four"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/capitalized-worth-monthly-yearly-four
site: BCT Engineering
---

# Capitalized worth and infinite-period deposit

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

- Asked in: 2076 Shrawan, 1.5+4.5 marks
- Video: [Capitalized Value - Engineering Economics Lightboard](https://www.youtube.com/watch?v=wsj7wC6QFbc) — 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-monthly-yearly-four
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-2

## Question

What is Capitalized Worth? How much rupees should we deposit in a bank so that we will be able to draw (i) Rs 6000 monthly (ii) Rs 100000 yearly and (iii) Rs 500000 in every four years for infinite period if bank interest rate is 0.75% per month?

## Short answer

Capitalized worth is present value for infinite uniform payments, CW = A/i. For monthly: 6,000/0.0075 = Rs 8,00,000; yearly effective rate 9.38% gives Rs 10,66,020; four-yearly effective rate 43.14% gives Rs 11,59,003; total deposit = Rs 30,25,023.

## Answer

#### Capitalized worth
Capitalized worth (CW) is the present worth of a series of cash flows that continues forever (infinite life). For a uniform end-of-period amount A at interest rate i per period:
**CW = P = A / i**
It is the sum which, when deposited, earns interest enough to pay A every period without reducing the principal. It is used for permanent structures such as dams, bridges and endowments.

#### Interest rates
Monthly i = 0.75%.
- Yearly effective rate: i_y = (1.0075)¹² − 1 = 9.3807%
- Four-yearly effective rate: i_4 = (1.0075)⁴⁸ − 1 = 43.1405%

#### (i) Rs 6,000 monthly
P₁ = 6,000 / 0.0075 = **Rs 800,000**

#### (ii) Rs 100,000 yearly
P₂ = 100,000 / 0.093807 = **Rs 1,066,020**

#### (iii) Rs 500,000 every four years
P₃ = 500,000 / 0.431405 = **Rs 1,159,003**

#### Total deposit
P = 800,000 + 1,066,020 + 1,159,003 = **Rs 3,025,023**

**Answer: Rs 800,000 for (i), Rs 1,066,020 for (ii), Rs 1,159,003 for (iii); total about Rs 30.25 lakh.** (First withdrawal of each series is taken at the end of the first period.)

## Check yourself

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

1. What is capitalized worth for uniform A?
   A. A x i
   B. A (F/A, i, n)
   C. Present worth of an infinite series, P = A/i
   D. A/(1+i)
   Answer: C. CW is the sum whose interest pays A each period forever. (Key point: Capitalized worth)

2. Why are yearly and four-yearly rates computed from 0.75% monthly?
   A. Because the bank pays simple interest
   B. To reduce the deposit
   C. Because withdrawals are made at the start
   D. Each withdrawal series needs an interest rate matching its own period
   Answer: D. i_y = (1.0075)^12 - 1 and i_4 = (1.0075)^48 - 1. (Key point: Effective rates)

3. What is P3 for Rs 500,000 every four years?
   A. 500,000 / 0.431405 = Rs 1,159,003
   B. 500,000 / 0.0075
   C. 500,000 / 0.093807
   D. 500,000 x 0.431405
   Answer: A. Divide by the four-year effective rate. (Key point: Four-yearly part)

4. What is the total deposit?
   A. Rs 8 lakh only
   B. About Rs 30.25 lakh, the sum of the three parts
   C. Rs 10.66 lakh
   D. Rs 11.59 lakh
   Answer: B. 800,000 + 1,066,020 + 1,159,003 = 3,025,023. (Key point: Total)

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