You are planning to save for retirement over the next 30 years. To save for reti

Question

You are planning to save for retirement over the next 30 years. To save for retirement, you will invest $1,150 per month in a stock account in real dollars and $540 per month in a bond account in real dollars. The effective annual return of the stock account is expected to be 13 percent, and the bond account will earn 6 percent. When you retire, you will combine your money into an account with an effective return of 8 percent. The returns are stated in nominal terms. The inflation rate over this period is expected to be 3 percent.

1.How much can you withdraw each month from your account in real terms assuming a 25-year withdrawal period? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

2.What is the nominal dollar amount of your last withdrawal? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Explanation / Answer

First we need to calculate the future value of both the accounts. The formula to be used:

FV = Pmt x [((1+r/n)nt -1))/(r/n)]
Where, PMT = Monthly deposits
r = interest rate
n = number of periods per year
t = number of years

Future value of Stock Account = $1,150 x ((1+0.13/12)360 -1))/0.13/12) = $5,029,260.25
Future value of Bond Account = $540 x ((1+0.06/12)360 -1))/0.06/12) = $250,356.06
Combined Value = $5,029,260.25 + $250,356.06 = $5,279,616.31

Real dollar amount withdrawal per month: Pmt = PV*(r/n) / (1-(1+r)-tn)

The amount you deposit is PV, the interest rate per period is r, the number of periods is n, the number of years is t, and Pmt is the payment per period.

r = effective interest – inflation => 8% - 3% = 5%

[($5,279,616.31 x 0.4167%) / (1-(1+0.4167%)-300)] = $30,865.34

Nominal dollar amount withdrawal:

[($5,279,616.31 x 0.6667%) / (1-(1+0.6667%)-300)] = $40,750.34

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.