Question

You are planning your retirement in 10 years. You currently have $164,000 in a bond account and $604,000 in a stock account. You plan to add $7,600 per year at the end of each of the next 10 years to your bond account. The stock account will earn a return of 10.5 percent and the bond account will earn a return of 7 percent. When you retire, you plan to withdraw an equal amount for each of the next 21 years at the end of each year and have nothing left. Additionally, when you retire you will transfer your money to an account that earns 6.25 percent.How much can you withdraw each year in your retirement? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

$179,409.81

Explanation:

The computation of annual withdrawal is shown below:-

Future value of annuity = Annual investment in bond × FVA (10%, 7)

= $7,600 × 13.81645

= 105,005.00

Refer to the Future value of annuity table

Now Future value of the existing balance

= $164,000 × (1.07^10)

= $322,612.82

So, the total value of the bond investment in 10 years  is

= Future value of an annuity + Future value of the existing balance + value of the stock investment in 10 years

= $105,005 + $322,612.82 + $604,000 × (1.105^10)

=  $2,066,922.66

And, the PVIFA at 6.25% for 21 years is 11.52068

So, the annual withdrawal is

=  total value of the bond investment in 10 years  ÷  PVIFA at 6.25% for 21 years

= $2,066,922.66 ÷ 11.52068

= $179,409.81