Practice Question
Your 6-year-old wants to go to Princeton. This will cost you $30,000 per year for 4 years. On her next birthday you start putting money into an account paying 14% annually and continue to deposit the same amount every year until her 17th birthday. The first tuition payment will be payable on her 18th birthday, the second on her 19th birthday etc. How large are your annual deposits to this account?
Step 1: Present Value of Tuition Costs at Age 17
Tuition payments: $30,000 on the 18th, 19th, 20th, and 21st birthdays.
We discount each back to age 17:
\[
PV = \frac{30,000}{(1.14)^1} + \frac{30,000}{(1.14)^2} + \frac{30,000}{(1.14)^3} + \frac{30,000}{(1.14)^4}
\]
\[
PV = 26,315.79 + 23,081.40 + 20,240.71 + 17,773.47 = 87,411.37
\]
Step 2: Find the Annual Deposit Amount
You make 11 deposits, from age 7 to 17. These deposits grow at 14% annually.
Use the Future Value of Annuity Formula:
\[
FV = PMT \times \frac{(1 + r)^n - 1}{r}
\]
\[
87,411.37 = PMT \times \frac{(1.14)^{11} - 1}{0.14} = PMT \times 23.046
\]
\[
PMT = \frac{87,411.37}{23.046} \approx 3,793.15
\]
Conclusion: To accumulate enough for Princeton tuition, you must deposit $3,793.15 every year for 11 years starting on your daughter’s 7th birthday.