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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.

Respuesta :

Answer:

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

                 

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