Chapter 17.1, Problem 39E

Individual Retirement Accounts The multiplier function

          $M=\frac{{\left(1+i\right)}^n\left(1-t\right)+t}{{\left[1+\left(1-t\right)i\right]}^n}$

compares the growth of an Individual Retirement Account (IRA) with the growth of the same deposit in a regular savings account. The function M depends on the three variables n, i, and t, where n represents the number of years an amount is left at interest, i represents the interest rate in both types of accounts, and t represents the income tax rate. Values of M > 1 indicate that the IRA grows faster than the savings account. Let M = f(n, i, t) and find the following.

39.    What is the multiplier when money is invested for 40 years at 6% interest and the income tax rate is 28%? Which account grows faster?