Answer:
a. Assuming a 3% per year real earnings rate for the fixed-income fund and 6% per year for common stocks, what will be George’s expected accumulation in each account at age 65?
Fixed Income Fund:
$100,000 x (1 + 3%)²⁵ = $209,377.79
$1,500 x 36.459 (FV annuity factor, 3%, 25 periods) = $54,688.50
total value = $264,066.29
Common Stock Fund:
$100,000 x (1 + 6%)²⁵ = $429,187.07
$1,500 x 54.865 (FV annuity factor, 6%, 25 periods) = $82,297.50
total value = $511,484.57
b. What will be the expected real retirement annuity from each account, assuming these same real earnings rates?
Contribution from fixed income fund:
$264,066.29 = annual payment x 11.938 (PV annuity factor, 3%, 15 periods) annual payment = $264,066.29 / 11.938 = $22,119.81
Contribution from common stock fund:
$511,484.57 = annual payment x 9.7122 (PV annuity factor, 6%, 15 periods) annual payment = $511,484.57 / 9.7122 = $52,664.13
c. If George wanted a retirement annuity of $30,000 per year from the fixed-income fund, by how much would he have to increase his annual contributions?
total fixed income fund = $30,000 x 11.938 = $358,140
difference in value = $358,140 - $264,066.29 = $94,073.71 / 36.459 = $2,580.26
difference in annual contributions = $94,073.71 /
