1 (of 11) 1 value 100 points Problem 6-32 Calculating Annuities [LO1] You are pl
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1 (of 11) 1 value 100 points Problem 6-32 Calculating Annuities [LO1] You are planning to save for retirement over the next 35 years. To do this, you will invest $900 per month in a stock account and $500 per month in a bond account. The return of the stock account is expected to be 11 percent, and the bond account will pay 7 percent. When you retire, you will combine your money into an account with a 8 percent return. How much can you withdraw each month from your account assuming a 30-year withdrawal period? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g, 32.16.) Withdrawal per month d References eBook & Resources Worksheet Dihicully intermediate Problem 6-32 Calculating Leanw objective: 06:01 Ho ?Type here to searchExplanation / Answer
Monthly investment in stock = $900
Number of monthly deposit in bonds = 35 years *12 = 420
Monthly interest rate for bonds = 9%/12 = 0.75% = 0.0075
Future value of annuity = Annuity amount * {(1+r)n-1}/r
Value of stock investment at the end of 35 years = $900*(1.0075420-1)/0.0075 = $2,647,606.03
Monthly investment in bonds = $500
Number of monthly deposit in bonds = 35 years *12 = 420
Monthly interest rate for bonds = 7%/12 = 0.5833% = 0.005833
Value of bond investment at the end of 35 years = $500*(1.005833420-1)/0.005833 = $900,527.30
Total money at the end of 35 years = $2,647,606.03 + $900,527.30 = $3,548,133.33
Monthly interest rate after retirement = 8%/12 = 0.6667% = 0.006667
Number of monthly withdrawals after retirement = 30 years * 12 = 360
The monthly withdrawals shall be calculated in such a way that the present value of monthly withdrawals is the amount invested at the time of retirement
Present value of annuity = Annuity amount * {1-(1+r)-n}/r
$3,548,133.33 = Monthly withdrawals * (1-1.006667-360)/0.006667
$3,548,133.33 = Monthly withdrawals * 136.2835
Monthly withdrawals = $3,548,133.33/136.2835 = $26,034.95
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