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.

Question

Freedom

Business

24 December, 00:33

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.

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Answers (1)

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Leonard Riley · Answer 1

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