Q3.31

Reginald is expecting steady growth of 10% per year in profits from his new company. All

profits are going to be invested at 20% interest. If profits for this year (at the end of the year)

total $1,000,000, how much will be saved at the end of 10 years?

Solution:

This is a geometric gradient series.

The growth adjusted interest rate i

0

= (1+i)/ (1+g) - 1 = (1 + 20%)/(1 + 10) - 1 = 9.09% >0

Since i

0

is positive, we can use the factor table.

P = A (P/A, i

0

, N) / (1+g) = 1,000,000 (P/A, 9.09%, 10)/ (1+10%) = 1,000,000 * 6.3923/1.1 =

5,811,182

F = P (F/P, i, N) = 5,811,182 (F/P, 20%, 10) = 5,811,182 *6.1917 = 35,981,094

My question is, where did the 6.3923 come from??