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Suppose you want to invest enough over each of the next 40 yearsto generate an...

Suppose you want to invest enough over each of the next 40 years to generate an annual retirement payment of $40,000 per year for 20 years. If you can earn a 6% rate of return, how much do you need to invest each year?

Select one:

a. $40,000

b. $458,796

c. $2,965

d. $16,361

Solutions

Expert Solution

Present value of annuity amount after retirement=Annuity payment*((1-(1/(1+r)^n))/r)

where

r-discount rate per period=6%

n-number of periods -20

Annuity payment-40000

Putting values

Present value of annuity amount after retirement=40000*((1-(1/(1+.06)^20))/.06)

=458796.85

Now the future value of the deposits before the retiorement shou;ld be equal to Present value of annuity amount after retirement

Future value of annuity=Annuity amount*(((1+r)^n)-1)/r

where

r-discount rate per period=6%

n-number of periods -40

Future value of annuity=Present value of annuity amount after retirement=458796.85

Putting values

458796.85=Annuity amount*(((1+.06)^40)-1)/.06

Solving we get annuity amount=$2,964.53

Thus correct answer is $2,965

jeff jeffy answered 2 years ago
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