Respuesta :
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).
[tex]FV=\frac{A((1+r)^{n}-1) }{r}[/tex]
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.
[tex]FV=\frac{800((1+0.11)^{30}-1) }{0.11} = 159,216.70[/tex]
In the case of the bond account it should look like this.
[tex]FV=\frac{400((1+0.07)^{30}-1) }{0.07} = 37,784.31[/tex]
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.
[tex]Real(r)=\frac{[1+Nominal(r)]}{[1+Inflation(r)]} -1=\frac{(1+0.09)}{(1+0.04)} -1=0.0481[/tex]
This is 4.81% effective annual rate, but we need this rate to be effective monthly, that is:
[tex]r(monthly)=(1+r(annual))^{\frac{1}{12} } -1=(1+0.0481)^{\frac{1}{12} } -1=0.0039[/tex]
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.
[tex]PV=\frac{A((1+r)^{n} -1)}{r(1+r)^{n} } =\frac{A(2.234662443)}{0.012682296} =A(176.2032975)[/tex]
[tex]197,001.02=A(176.2032975)[/tex]
[tex]A=1,118.03[/tex]
Best of luck
