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Mutual fund from growing salary, 15 years

Short answer

With 7% annual salary growth, using the geometric series formula, the future amount is Rs 2,363,694. With an annual salary increase of Rs 25,000, using gradient and annuity factors, it is Rs 2,427,248.

Ramesh, a Civil Engineer, is planning to place a total of 20% of his salary, which is Rs. 250000 per year now, each year in mutual fund. He expects 7% salary increase each year for next 15 years. If the mutual fund will average 10% annual return, what will be the sum-amount at the end of 15 years? If salary increases by Rs. 25000 per year, what will be the amount?

Assumption: the first deposit is at the end of year 1 and equals 20% of the present salary: A₁ = 0.20 × 2,50,000 = Rs 50,000. Later deposits grow with the salary. Interest i = 10%, n = 15 years.

(a) Salary grows 7% per year (geometric series)

 deposits:  50,000   50,000(1.07)   50,000(1.07)²  ...  50,000(1.07)^14
 year:         1          2              3         ...        15

For a geometric series with growth g ≠ i:

F = A₁ [(1 + i)^n − (1 + g)^n] / (i − g)

  • (1.10)^15 = 4.17725; (1.07)^15 = 2.75903
  • F = 50,000 × (4.17725 − 2.75903) / (0.10 − 0.07)
  • F = 50,000 × 47.2739

Answer (a): F = Rs 2,363,694 (about Rs 23.64 lakh).

(b) Salary increases by Rs 25,000 every year (gradient)

The deposit rises by 20% × 25,000 = Rs 5,000 each year: G = 5,000.

 deposits: 50,000, 55,000, 60,000, ... , 50,000 + 14(5,000) = 1,20,000
  • (F/A, 10%, 15) = 31.7725
  • (A/G, 10%, 15) = 1/i − n/[(1 + i)^n − 1] = 5.2789
  • Uniform equivalent A = 50,000 + 5,000 × 5.2789 = Rs 76,394.67
  • F = A (F/A, 10%, 15) = 76,394.67 × 31.7725

Answer (b): F = Rs 2,427,248 (about Rs 24.27 lakh).

✓ Answer checked by Claude Opus 5.5 (high effort)

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