# You are planning your retirement in 10 years. You currently have \$169,000 in a bond account and \$609,000 in a stock account. You plan to add \$7,100 per year at the end of each of the next 10 years to your bond account. The stock account will earn a return of 10.75 percent and the bond account will earn a return of 7.25 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 6.5 percent. How much can you withdraw each year in your retirement

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## Question:

You are planning your retirement in 10 years. You currently have \$169,000 in a bond account and \$609,000 in a stock account. You plan to add \$7,100 per year at the end of each of the next 10 years to your bond account. The stock account will earn a return of 10.75 percent and the bond account will earn a return of 7.25 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 6.5 percent. How much can you withdraw each year in your retirement

\$187,584.20

Explanation:

Firstly, we need to calculate the total future value (FV) of the bond account and stock account after 10 year from now (when you come to retirement age):

FV_bond at retirement = 169,000 x (1 + 7.25%)^10 + 7,100 x (1 + 7.25%)^9 + 7,100 x (1 + 7.25%)^8 + … 7,100 x (1 + 7.25%)^0 = 426,230.93

FV_stock at retirement = 609,000 x (1 + 10.75%)^10 = 1,690,653.63

Total FV of your investment portfolio = 2,116,884.57

Because you plan to use up all the funds in your account after 21 equal amount withdrawals after retirement, total present value (at the time you retire not now) of these withdrawals (discounted at 6.5%) have to be equal to the value of your invesment 10 years from now, or:

2,116,884.57 = C/(1+6.5%) + C/(1+6.5%)^2 + … + C/(1+6.5%)^21, with C is the amount you plan to withdraw each year.

Solve the equation we get C = 187,584.20

Note: The equation can be solved easily using Excel or BAII Plus.

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