---
title: "Find A from cash flow with 25000, 5A, 10000"
subject: "Engineering Economics"
chapter: 2
key: "semester_6/engineering_economics:find-a-25000-5a-10000"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/find-a-25000-5a-10000
site: BCT Engineering
---

# Find A from cash flow with 25000, 5A, 10000

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

- Asked in: 2065 Chaitra, 8 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/engineering_economics/find-a-25000-5a-10000
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-2

## Question

Find the value of A if i = 15%.
[Figure: outflow of 25000 at year 0; uniform receipts A at years 0 to 6 (seven arrows); outflow of 5A at year 10; receipt of 10000 at year 15]

## Short answer

Set present worth of receipts equal to outflows: A[1+(P/A,15%,6)] + 10000(P/F,15%,15) = 25000 + 5A(P/F,15%,10). Solving gives A = Rs 6,698.79.

## Answer

#### Reading the diagram
Year 0: outflow 25,000 and a receipt A (uniform series of seven receipts A at years 0 to 6). Year 10: outflow 5A. Year 15: receipt 10,000. Equivalence at i = 15% means PW of receipts = PW of outflows.

```text
 receipts : A A A A A A A (yr 0-6)         10,000 (yr 15)
 outflows : 25,000 (yr 0)        5A (yr 10)
```
#### Factors (i = 15%)
- (P/A, 15%, 6) = 3.7845
- (P/F, 15%, 10) = 0.2472
- (P/F, 15%, 15) = 0.1229

#### Equation
A + A (P/A, 15%, 6) + 10,000 (P/F, 15%, 15) = 25,000 + 5A (P/F, 15%, 10)

- A (1 + 3.7845) + 10,000 × 0.1229 = 25,000 + 5A × 0.2472
- 4.7845 A + 1228.94 = 25,000 + 1.2359 A
- (4.7845 − 1.2359) A = 25,000 − 1228.94
- 3.5486 A = 23771.06

**Answer: A = Rs 6,698.79.**

## Check yourself

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

1. How many A receipts?
   A. Six
   B. A(P/A,15%,7)
   C. One
   D. Seven, years 0 to 6: A + A(P/A,15%,6)
   Answer: D. A at year 0 plus six. (Key point: Receipts at 0-6)

2. Equation?
   A. A + A(P/A,15%,6) + 10,000(P/F,15%,15) = 25,000 + 5A(P/F,15%,10)
   B. A(P/A,15%,6) = 25,000
   C. A + 10,000 = 25,000 + 5A
   D. A(F/A) = 25,000
   Answer: A. PW receipts = PW outflows. (Key point: Equation)

3. How is 5A at year 10 brought to year 0?
   A. 5A x 0.1229
   B. 5A x (P/F,15%,10) = 5A x 0.2472
   C. 5A x (F/P,15%,10)
   D. 5A x 3.7845
   Answer: B. Discount 10 years. (Key point: Moving 5A)

4. A?
   A. Rs 25,000
   B. Rs 3,548
   C. About Rs 6,698.79
   D. Rs 23,771
   Answer: C. A = 23,771.06/3.5486. (Key point: Result)

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