- 2065 Chaitra · 8 marks
Find A from cash flow with 25000, 5A, 10000
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.
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]
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.
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.
✓ Answer checked by Claude Opus 5.5 (high effort)
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