You are planning your retirement in 10 years. You currently have $167,000 in a b

Question

You are planning your retirement in 10 years. You currently have $167,000 in a bond account and $607,000 in a stock account. You plan to add $7,300 per year at the end of each of the next 10 years to your bond account. The stock account will earn a return of 11.25 percent and the bond account will earn a return of 7.75 percent. When you retire, you plan to withdraw an equal amount for each of the next 23 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 7 percent.

Required: How much can you withdraw each year in your retirement?

Explanation / Answer

Value of stock account after 10 years=607,000*(1.1125)10=1762742.55

Value of bond account after 10 years=167,000 *(1.0775)10+ 7,300*((1.0775)9+(1.0775)8+........+(1.0775)0)

Value of bond account after 10 years=167,000 *(1.0775)10+ 7,300*(((1.0775)10-1)/.0775) =352281.03+104504.66 = 456785.69

Total Value of account after 10 years=Value of stock account after 10 years+Value of bond account after 10 years= 1762742.55+456785.69=2219528.24

The equal amount for each of the next 23 years at the end of each year that he withdrew after retirement=A

Total Value of account after 10 years at retirement=B=2219528.24

rate of interest=r=7%,Total time=T=23

A=B*r/(1-(1/(1+r)T))

A=2219528.24*.07/(1-(1/(1.07)23))

A=196903.07

Thus you can withdraw $196,903 each year in your retirement.

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