You are planning to save for retirement over the next 30 years.
To do this, you will invest $830 per month in a stock account and
$430 per month in a bond account. The return of the stock account
is expected to be an APR of 10.3 percent, and the bond account will
earn an APR of 6.3 percent. When you retire, you will combine your
money into an account with an APR of 7.3 percent. All interest
rates are compounded monthly.
How much can you withdraw each month from your account assuming a
withdrawal period of 25 years? (Do not round intermediate
calculations and round your answer to 2 decimal places, e.g.,
32.16.)
Withdrawal $
per month
Stock Account:
Deposit Values = $ 830, Frequency = Monthly, APR = 10.3 % or (10.3 /12) ~ 0.8583 % per month, Compounding Frequency = Monthly, Tenure = 30 years or 360 months
Total FV of STock Account = S = 830 x (1.008583)^(359) + 830 x (1.008583)^(358) + ............+ 830 x (1.008583) + 830 = $ 2000453.11
Bond Account:
Deposit Values = $ 430, Frequency = Monthly, APR = 6.3 % or (6.3 /12) ~ 0.525 % per month, Compounding Frequency = Monthly, Tenure = 30 years or 360 months
Total FV of Bond Account = B = 430 x (1.00525)^(359) + 430 x (1.00525)^(358) + ............+ 430 x (1.00525) + 430 = $ 457579.27
Total Account Value Upon Retirement = B + S = 457579.27 + 2000453.11 = $ 2458032.37
Retirement Account Rate = 7.3 % or (7.3 / 12 ) ~ 0.6083 % per month and Withdrawal Tenure = 25 years or 300 months
Let the monthly wihdrawals be $ K
Therefore, 2458032.37 = K x (1/0.006083) x [1-{1/(1.006083)^(300)}]
K = $ 17845.45
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