Question

1. Northeastern costs approximately $50,000 per year for a four-year program, whether completed in four years or five. Assume that a student’s parents realized 15 years ago that college was going to cost $50,000 per year for four years, and wondered how much they would have to save each year to have the money to pay for the student’s education. The assumption is that payments are made into the college fund each year (as an ordinary annuity), and payments are withdrawn from the fund at the end of the relevant years.
   
   The key information for this scenario is as follows:
   1. The number of years of contributions is 18.
   2. Assume for simplicity that the college payments will be made at the end of years 15, 16, 17, and 18, that is just after each deposit in those years.
   3. The interest rate is 10 percent.
   4. College costs are $50,000 per year, and are assumed to be the same for each of the four years.

Using the key information for the scenario above, how much would the parents have to save each year for 18 years to have exactly the amount of money needed to pay the student’s expenses? (Solve for the annual savings that will exactly match the amount saved to the amount needed for college.) Be sure to include your calculation formulas in your answer.

Answer 1

We need to equate the PV of an ordinary year-end annuity of ( annual) savings & the PV of the 4 $ 50000 withdrawals at end of Yrs. 15,16,17& 18

so, PV of the annuity of

an amt. "x "

for a period of n= 18

at an interest rate of r= 10% p.a.

using the formula,

PV(OA)=Pmt.*(1-(1+r)^-n)/r

& substituting the above values,

x*(1-1.1^-18)/0.1=(50000/1.1^15)+(50000/1.1^16)+(50000/1.1^17)+(50000/1.1^18)

& solving for x, we get the annual savings (for 18 yrs.) as

5088.91

ie. $ 5089