Question

You want to start saving for your daughter's college education now. She will enter college at age 18 and will pay fees of $4,000 at the end of each of the four years. You will start your savings by making a deposit in one year and at the end of every year until she begins college. If annual deposits of $2,458.79 will allow you to reach your goal, how old is your daughter now? Assume you can earn 6% annual interest on your savings. (Hints: You will need to do this in 2 stages. The fees for the 4 years of college need to be discounted back to year 18. Then you can determine the FV of the annual deposits, and calculate the number of payments needed. Ensure the sign of FV and PMT are different)

Answer 1

Using financial calculator

PMT=4000

N=4

I/Y=6%

CPT PV=13860.42

Now,

FV=13860.42

PMT=-2458.79

I/Y=6%

PV=0

CPT N=5

ALTERNATIVELY Using mathematical formula:

2458.79/6%*(1.06^t-1)=4000/1.06+4000/1.06^2+4000/1.06^3+4000/1.06^4

=>t=5

So, the daughter is 13 years old now