Problem 2. George More is a participant in a defined contribution pension plan t
ID: 2789183 • Letter: P
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Problem 2. 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 $1,500 per year to each. He plans to retire at age 65, and his life expectancy is age 80. 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 657 (10 points. Round your final answer to the nearest dollar amount.) a. What will be the expected real retirement annuity from each account, assuming these same real earnings rates? (20 points. Round your final answer to the nearest dollar amount.) b. 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? (20 points. Round your final answer to the nearest dollar amount.) c.Explanation / Answer
a) Using FV function on a calculator, we can compute the values of both funds at age 65
N = 25, PMT = 1,500, PV = 100,000, I/Y = 3% => Compute FV = $264,067 is the value of fixed income fund
N = 25, PMT = 1,500, PV = 100,000, I/Y = 6% => Compute FV = $511,484 is the value of common stock fund
b) Annuity can be calculated using PMT function
N = 15, PV = 264,067, FV = 0, I/Y = 3% => Compute PMT = $22,120 from fixed income fund
N = 15, PV = 511,484, FV = 0, I/Y = 6% => Compute PMT = $52,664 from common stock fund
c) If he wants $30,000, the amount he must have at age 65 can be calculated using PV function
N = 15, PMT = 30,000, I/Y = 3%, FV = 0 => Compute PV = $358,138
Annual contribution can be calculated using PMT function
N = 25, I/Y = 3%, PV = -100,000, FV = 358,138 => Compute PMT = $4,080 should be his annual contribution
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