To calculate the amount that the client needs to set aside today to pay for four years of tuition and fees, we can use the future value formula:
FV = PV x (1 + r)^n
where FV is the future value, PV is the present value, r is the interest rate, and n is the number of compounding periods.
In this case, the present value is the current tuition and fees of $47,595. The interest rate is the client's expected rate of return of 8.7 percent. The number of compounding periods is the number of years until college, which is 6 years, and the inflation rate is 1.6 percent.
First, we need to calculate the future value of tuition and fees after 6 years, including inflation. This can be done using the formula:
FV = PV x (1 + inflation rate)^n
FV = $47,595 x (1 + 0.016)^6
FV = $54,187.29
Next, we need to calculate the total amount needed to pay for four years of tuition and fees. This can be done by multiplying the future value of tuition and fees by 4:
Total amount needed = $54,187.29 x 4
Total amount needed = $216,749.16
Finally, we need to calculate the amount that the client needs to set aside today to achieve this future value. This can be done by rearranging the future value formula:
PV = FV / (1 + r)^n
PV = $216,749.16 / (1 + 0.087)^6
PV = $136,276.89
Therefore, the client needs to set aside $136,276.89 today to pay for four years of tuition and fees after 6 years, assuming current tuition and fees are $47,595, and inflation for college costs averages 1.6 percent, and she can earn 8.7 percent on the money she invests for this purpose.