Question

You are planning to save for retirement over the next 30 years. To save for retirement, you will invest $800 per month in a stock account in real dollars and $400 per month in a bond account in real dollars. The effective annual return of the stock account is expected to be 11 percent, and the bond account will earn 7 percent. When you retire, you will combine your money into an account with an effective return of 9 percent. The returns are stated in nominal terms. The inflation rate over this period is expected to be 4 percent. How much can you withdraw each month from your account in real terms assuming a 25-year withdrawal period

Answer 1

Answer:

Ans. You withdraw each month from your account, for 300 months (25 years) $1,118.03 taking into account the expected inflation rate.

Explanation:

Hi, ok, first, we need to find out how much money will you have after saving in both accounts for 30 years, for that, we need to use the following equation and solve for FV (future value).

$FV=\frac{A((1+r)^{n}-1) }{r}$

Where, A is the amount saved in the account, r is the interest rate that it pays, n are the yearly equal payments, in our case 30. Everything should look like this in the case of the stock account.

$FV=\frac{800((1+0.11)^{30}-1) }{0.11} = 159,216.70$

In the case of the bond account it should look like this.

$FV=\frac{400((1+0.07)^{30}-1) }{0.07} = 37,784.31$

This means that after 30 years you will have $197,001.02

Now, we need to find the amount of monthly withdraw that you can make given the money saved, but in order to take into account the time value of money, we need to use the real rate of return and not the nominal rate of return (9%, when you gather all your money and send it to another acoount). Therefore, we have to find out the real rate of return, like this.

$Real(r)=\frac{[1+Nominal(r)]}{[1+Inflation(r)]} -1=\frac{(1+0.09)}{(1+0.04)} -1=0.0481$

This is 4.81% effective annual rate, but we need this rate to be effective monthly, that is:

$r(monthly)=(1+r(annual))^{\frac{1}{12} } -1=(1+0.0481)^{\frac{1}{12} } -1=0.0039$

That is 0.39% effective monthly, and we have to use the following equation with n=300 months, r=0.0039, PV= $197,001.02 and solve for A.

$PV=\frac{A((1+r)^{n} -1)}{r(1+r)^{n} } =\frac{A(2.234662443)}{0.012682296} =A(176.2032975)$

$197,001.02=A(176.2032975)$

$A=1,118.03$

Best of luck