213.4
4.You're saving to buy a house. You figure that you will need $20,000 to cover closing costs and the down payment. Assume that you can earn 12%, compounded monthly. If you save $300 per month starting the month after graduation, in 8 years will you have enough money to buy the house? (6 pts.)
Calculate the PV of the payments. r=.12/12, n = 96, P3 = 300
\( \Large PV = 300 \left [ \frac{1}{\frac{.12}{12}} - \frac{1}{\frac{.12}{12} \left(1+\frac{.12}{12} \right )^{96} } \right ] = 18{,}458.31 \).
Then determine what this PV will be worth in 8 years (find FV):
\( \Large FV = 18{,}458.31 \left(1+\frac{.12}{12} \right)^{96} = $47{,}978.19 \)
Plenty of money for the house.