Question

you are planning to save for retirement over the next 25 years. to do this, you will invest $790 per month in a stock account and $390 per month in a bond account. the return of the stock account is expected to be 9.9 percent, and the bond account will earn 5.9 percent. when you retire, you will combine your money into an account with an annual return of 6.9 percent. all interest rates are aprs with monthly compunding. how much can you withdraw each month from your account assuming a 20-year withdrawal period? (do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Calculate the future value of both the stock and bond investments using the future value of an annuity formula. Combine these to find total retirement savings. Then, using the retirement savings and interest rate for the 20-year withdrawal period, calculate the monthly withdrawal with the present value of an annuity formula.

Step-by-step explanation:

The student is seeking to understand how much can be withdrawn monthly in retirement after saving a certain amount per month for 25 years in stock and bond accounts with specific interest rates and monthly compounding. For the stock account with a 9.9% APR, and the bond account with a 5.9% APR, we need to calculate the future value of these periodic investments using the future value of an annuity formula. After retiring, the total amount will be combined into an account with a 6.9% return, from which withdrawals will take place over a 20-year period. To find the monthly withdrawal amount, the student must compute the present value of an annuity based on the total accumulated amount and the new interest rate.

To solve the student's problem, first calculate the future value of each annuity (stock and bond investments) separately. Then sum these amounts to find the total retirement savings. Finally, calculate the monthly withdrawal using the total amount and the 20-year withdrawal period interest rate of 6.9% with the present value of an annuity formula.