- 2066 Magh · 8 marks
Find G for gradient series with 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.
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]
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.
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.
✓ Answer checked by Claude Opus 5.5 (high effort)
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