When Steve and Roslyn retire together they wish to receive $40,000 additional income (in the equivalent of today’s dollars) at the beginning of each year. They assume inflation will be 4% and they expect to realize an after tax return of 8%. Based on life expectancies, they estimate their retirement period to be about 30 years. They want to know how much they will need to have in their fund at the time of their retirement.

Question

When Steve and Roslyn retire together they wish to receive $40,000 additional income (in the equivalent of today’s dollars) at the beginning of each year. They assume inflation will be 4% and they expect to realize an after tax return of 8%. Based on life expectancies, they estimate their retirement period to be about 30 years. They want to know how much they will need to have in their fund at the time of their retirement.

a. $698,457.24.

b. $728,299.37.

c. $731,894.20.

d. $813,529.88.

Answer 1

To calculate the amount Steve and Roslyn will need to have in their fund at the time of their retirement, you can use the future value of an annuity formula. Here's how you can do it step by step:

1. Convert the additional income they wish to receive into future dollars by accounting for inflation. Since they want $40,000 in today's dollars, you can calculate the future value by multiplying it with the inflation factor. In this case, it will be $40,000 * (1 + 0.04) = $41,600.

2. Determine the number of compounding periods, which in this case is the number of years they expect their retirement period to be, i.e., 30 years.

3. Calculate the interest rate after taxes. If they expect a pre-tax return of 8%, you need to factor in the effect of taxes. Let's say the tax rate is 25%, then the after-tax return rate will be 8% * (1 - 0.25) = 6%.

4. Now, you can use the future value of an annuity formula to calculate the required fund amount. The formula is FV = P * [(1 + r)^n - 1] / r, where FV is the future value, P is the annual payment, r is the interest rate per period, and n is the number of periods. Plugging in the values we have, FV = $41,600 * [(1 + 0.06)^30 - 1] / 0.06.

5. Calculate the expression in the brackets first, i.e., (1 + 0.06)^30 - 1 = 5.1423.

6. Divide the result from step 5 by the interest rate, 5.1423 / 0.06 = 85.705.

7. Finally, multiply the annual payment ($41,600) by the result from step 6 to get the required fund amount: $41,600 * 85.705 = $3,565,484.8.

So, the answer is not listed among the options provided. None of the options matches the calculated result of $3,565,484.8.