1 of 11 1 value 100 points Problem 632 Calculating Annuities

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 search

Solution

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