You have just retired with savings of $1.5 million. If you expect to live for 30 years and to earn 8% a year on your savings, how much can you afford to spend each year? Assume that you spend the money at the start of each year.

The amount I can afford to spend each year is $133,241.15

Explanation:

The amount I can afford to spend each year can be determined using the formula for present value of annuity due which is given below:

PV (Annuity due) = A * (1 - (1+r) ^-N) / r

PV is the present value of the investment which is $1.5 million

A is the annual spending which is unknown

r is the rate of return on the investment at 8% per year

N is the duration of investment which is 30 years

The formula can be rewritten as

A=PV / (1 - (1+r) ^-N) / r

(1 - (1+r) ^-N) / r=1 - (1+8%) ^-30/8%

=1 - (1+0.08) ^-30/0.08

= (1-0.099377333) / 0.08

=11.25778334

11.25778334 is known as annuity factor

A=$1500000/11.25778334

A=$133,241.15