Question

8. A computer company wants to have $2.1 million available 5 years from now to upgrade the system. The company expects to set aside uniformly increasing amounts of money each year to meet its goal. If the amount set aside at the end of year 1 is $50,000, how much will the constant increase have to be each year? Assume the investment account grows at a rate of 18% per year. Draw cash flow diagram.

Answer 1

Here, given, F = $2.1 million = $2,100,000

                     A₁ = $50,000

                     i = 18%

                     n = 5

                     G = ?

[A₁ + G(A/G, i, n)] * (F/A, i, n) = F

[50,000 + G(A/G, 18%, 5)] * (F/A, 18%, 5) = 2,100,000

[50,000 + G(1.673)] * 7.154 = 2,100,000

50,000 + 1.673G = 2,100,000 / 7.154 = 293,542.07

1.673G = 293,542.07 - 50000 = 243,542.07

G = 243,542.07 / 1.673 = $145,572.07

Thus, the constant increase have to be each year is $145,572.07.