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You are planning your retirement in 10 years. You currently have $173,000 in a bond account and $613,000 in a stock account. You plan to add $6,700 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 22 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.
1. How much can you withdraw each year in your retirement?

Respuesta :

TomShelby

Answer:

C  $ 185,846.980

Explanation:

Future value of the investment:

Stock Account:

[tex]Principal \: (1+ r)^{time} = Amount[/tex]

Principal 613,000.00

time 10.00

rate 0.10750

[tex]613000 \: (1+ 0.1075)^{10} = Amount[/tex]

Amount 1,701,758.09

Bond Account

Annuity component

[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]

C 6,700.00

time 10

rate 0.0725

[tex]6700 \times \frac{1-(1+0.0725)^{-10} }{0.0725} = PV\\[/tex]

PV $93,670.5376

lump sum component

[tex]Principal \: (1+ r)^{time} = Amount[/tex]

Principal 173,000.00

time 10.00

rate 0.07250

[tex]173000 \: (1+ 0.0725)^{10} = Amount[/tex]

Amount 348,352.64

Total future value:

1,701,758.09  +  93,670.5376  +  348,352.64 =  2.143.781,27

Withdrawals over the course of 22 years:

[tex]PV \div \frac{1-(1+r)^{-time} }{rate} = C\\[/tex]

PV 2,143,781.27

time 22

rate 0.065

[tex]2143781.27 \div \frac{1-(1+0.065)^{-22} }{0.065} = C\\[/tex]

C  $ 185,846.980