Question

Assume that you make $50,000 per year. You expect your pay to increase by 2.5% year from now until you retire in 30 years. Your goal is to withdraw an amount equal to 80% of your annual income at retirement each year for 25 years (assume withdrawals are made at the end of each year in retirement). How much would you have to invest each year from now until retirement if your investment returns are 8% per year while working and 6% per year while retired.

Answer 1

First, we calculate the annual income at retirement.

Future value = present value * (1 + growth rate)^{number of years}

Future value = $50,000 * (1 + 2.5%)³⁰ = $104,878.38

Income required during retirement = 80% of annual income at retirement

Income required during retirement = 80% * $104,878.38 = $83,902.70

First, we calculate the amount required at retirement to enable the yearly withdrawals during retirement. The amount required at retirement is calculated using PV function in Excel :

rate = 6% (rate of return earned during retirement)

nper = 25 (number of years in retirement)

pmt = -83902.70 (yearly withdrawal. This is entered with a negative sign because it is a withdrawal)

PV is calculated to be $1,072,558.10

Next, we calculate the yearly saving required to accumulate the required amount at retirement. The yearly saving required is calculated using PMT function in Excel :

rate = 8% (rate of return earned until retirement)

nper = 30 (number of years until retirement)

pv = 0 (amount currently saved is zero)

fv = 1072558.10 (required amount at retirement)

PMT is calculated to be $9,467.94

The amount to invest each year from now until retirement is $9,467.94