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Find A and G with A = 3G

Short answer

Set present worth of receipts equal to 50,000: A(P/A,10%,10) + 2G(P/G,10%,5)(P/F,10%,3) = 50,000. With A=3G, G = Rs 1,739.47 and A = Rs 5,218.40.

Find the value of A and G if i = 10%. A = 3G. [Figure: outflow of 50000 at year 0; receipts at years 1 to 10 shown on the diagram: a uniform amount A each year, plus a gradient series that begins after year 3 and rises steadily (2G marked at year 5, 8G marked at year 8), with no gradient beyond year 8 (only A in years 9 and 10)]

Reading the diagram (assumption)

Outflow of Rs 50,000 at year 0. Receipts: uniform A in years 1 to 10, plus a gradient that is zero at year 4, 2G at year 5, 4G at year 6, 6G at year 7 and 8G at year 8 (increase of 2G per year), nothing after year 8. So the gradient series has gradient amount 2G, five terms (years 4 to 8), and its base is at year 3. The project is taken as just equivalent, PW of receipts = PW of outflow.

 receipts:  A  A  A  A  A+2G  A+4G  A+6G  A+8G   A   A
 year:      1  2  3  4    5     6     7     8     9   10
 outflow:  50,000 at year 0

Factors (i = 10%)

  • (P/A, 10%, 10) = 6.1446
  • (P/G, 10%, 5) = 6.8618 [(A/G, 10%, 5) = 1.8101, (P/A, 10%, 5) = 3.7908]
  • (P/F, 10%, 3) = 0.7513

Equation

PW of receipts = PW of outflow

A (P/A, 10%, 10) + 2G (P/G, 10%, 5)(P/F, 10%, 3) = 50,000

Put A = 3G:

  • 3G × 6.1446 + 2G × 6.8618 × 0.7513 = 50,000
  • 18.4337 G + 10.3107 G = 50,000
  • 28.7444 G = 50,000

Answer: G = Rs 1,739.47 and A = 3G = Rs 5,218.40.

✓ Answer checked by Claude Opus 5.5 (high effort)

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