Your daughter will be going to college in 12 years and you are starting a fund for her education. She will need $15,000 at the beginning of each year for four years. The fund earns 9% annually, compounded monthly, and you plan to make monthly deposits, starting at the end of the current month. How much should you deposit each month to meet her educational expenses? P.S. The parents will continue to make monthly deposits, while she continues her education, until the beginning of her 4th. year, when she withdraws her last payment of $15,000. Use only standard TVM formulas. Thanks and have a good day.
This is a relatively easy problem to solve. Since the daughter has 4 annual payments of $15,000 each, we simply find their PV using the standard TVM formula. One important thing to do is convert 9% from comp. monthly to annual compound, which comes to about 9.38%.
PV=$52,713.28. This is PV of her fund at the beginning of her college ed.
The formula used for this is this standard TVM formula:
PV=P{[1 + R]^N - 1.[1 + R]^-N} R^-1=PV OF $1 PER PERIOD.
Now, the above PV is 12 years from now. We have to find its PV as of today.
PV=$52,713.28[1+.09/12]^-144
PV=$17,973.48. This is the PV as of today. We now have to find the monthly payment required to give this PV for 15 years, or 15 x 12=180 months. For this, will use another standard TVM formula, which is this:
PMT=PV. R.{[1 + R]^N/ [1 + R]^N - 1}
PMT=$17,973.48 x 0.010142666
PMT=$182.30. This is the monthly deposit made by her parents.
