Question

George More is a participant in a defined contribution pension plan that offers a fixed-income fund and a common stock fund as investment choices. He is 40 years old and has an accumulation of $100,000 in each of the funds. He currently contributes $1,500 per year to each. He plans to retire at age 65, and his life expectancy is age 80.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? (Do not round time value factors and round your final answer to the nearest dollar amount.)Fixed Income FundCommon Stock Fundb. What will be the expected real retirement annuity from each account, assuming these same real earnings rates? (Do not round time value factors and round your final answer to the nearest dollar amount.)Fixed Income FundCommon Stock Fundc. 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? (Do not round time value factors and round your final answer to the nearest dollar amount.)

Answer 1

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 /