---
title: "Find G for gradient series with 4G at year 5"
subject: "Engineering Economics"
chapter: 2
key: "semester_6/engineering_economics:find-g-a-5000-4g"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/find-g-a-5000-4g
site: BCT Engineering
---

# Find G for gradient series with 4G at year 5

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

- Asked in: 2066 Magh, 8 marks
- Video: [Arithmetic Gradient - Engineering Economics Lightboard](https://www.youtube.com/watch?v=ykQ7M9UNuok) — 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/find-g-a-5000-4g
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-2

## Question

Find the value of G if i = 10%.
[Figure: outflow of 50000 at year 0; receipts at years 1 to 5: A = 5000 in each year, plus a gradient series of G starting at year 2 and rising by G each year, reaching 4G at year 5]

## Short answer

Equate present worth: 50,000 = 5,000(P/A,10%,5) + G(P/G,10%,5). With factors 3.7908 and 6.8618, G = (50,000 - 18,953.93)/6.8618 = Rs 4,524.48.

## Answer

#### Reading the diagram
Outflow Rs 50,000 at year 0. Receipts are a uniform A = Rs 5,000 for years 1 to 5, plus a gradient G that is 0 at year 1, G at year 2, 2G at year 3, 3G at year 4 and 4G at year 5. The project is taken as just equivalent: PW of receipts = PW of cost.

```text
 receipts:  5000  5000+G  5000+2G  5000+3G  5000+4G
 year:        1      2       3        4        5
 outflow: 50,000 at year 0
```
#### Factors (i = 10%, n = 5)
- (P/A, 10%, 5) = 3.7908
- (P/G, 10%, 5) = 6.8618

#### Equation
50,000 = 5,000 (P/A, 10%, 5) + G (P/G, 10%, 5)

- 50,000 = 5,000 × 3.7908 + G × 6.8618
- 50,000 = 18953.93 + 6.8618 G
- G = (31046.07) / 6.8618

**Answer: G = Rs 4,524.48 per year.**

## Check yourself

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

1. Receipts in year 1-5?
   A. 5,000 only
   B. G, 2G, 3G, 4G, 5G
   C. 5,000 + G each year
   D. 5,000 each year plus gradient 0, G, 2G, 3G, 4G
   Answer: D. Gradient starts at 0 in year 1. (Key point: Reading)

2. Equation?
   A. 50,000 = 5,000(P/A,10%,5) + G(P/G,10%,5)
   B. 50,000 = 5,000(F/A) + G(F/G)
   C. 50,000 = 5,000 + G
   D. 50,000 = G(P/A,10%,5)
   Answer: A. PW of receipts equals the outflow. (Key point: Equation)

3. (P/A,10%,5) and (P/G,10%,5)?
   A. 6.8618 and 3.7908
   B. 3.7908 and 6.8618
   C. 1.8101 and 3.7908
   D. 4.0 and 6.0
   Answer: B. Factors at 10%, n=5. (Key point: Factors)

4. G?
   A. Rs 5,000
   B. Rs 31,046
   C. Rs 4,524.48 per year
   D. Rs 6.86
   Answer: C. 31,046.07/6.8618. (Key point: Result)

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