Brian decides to set up a 401(k). For the next 25 years, he plans on depositing...

Brian decides to set up a 401(k). For the next 25 years, he plans on depositing $300 a month into the account that offers a 10.99% annual interest rate compounded monthly.

a)how much will he have at retirement

b) if he is taxed at a rate of 30%, how much will he have after taxes?

c) if he purchases an annuity with the money left after taxes that guarantees 8% interest compounded monthly for 20 years, how mych will he receive each month?

Expert Solution

a.
We would calculate the amount at retirement using future value of annuity formula
Future value of annuity	Annuity*[((1+r)^n)-1]/r
r represents interest rate and n represents no of payments
Monthly interest rate	0.92%	10.99%/12
No of payments	300	25*12
Calculation of future value of annuity
Future value of annuity	300*[((1+0.0092)^300)-1]/0.0092
Future value of annuity	300*1573.394
Future value of annuity	$472,018.21

b.
After tax amount received at maturity	472018.21*(1-0.30)
After tax amount received at maturity	$330,412.74

c.
Using the present value of annuity formula the monthly payment can be calculated
Present value of annuity	Annuity*[1-((1+r)^-n)]/r

Monthly interest rate	0.67%	8%/12
No of payments	240	20*12

Annuity	330412.74/[1-(1.0067^-240)]/0.0067
Annuity	330412.74/119.5543
Annuity	$2,763.70

Thus, monthly amount received would be $2,763.70.

ekkarill92 answered 1 year ago

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