Question

Present value. Prestigious University is offering a new admission and tuition payment plan for all alumni. On the birth of a​ child, parents can guarantee admission to Prestigious if they pay the first​ year's tuition. The university will pay an annual rate of return of 5.5 ​% on the deposited​ tuition, and a full refund will be available if the child chooses another university. The tuition is expected to be ​$14,000 a year at Prestigious 20 years from now. What would parents pay today if they just gave birth to a new baby and the child will attend college in 20 ​years? How much is the required payment to secure admission for their child if the interest rate falls to 3.5 ​%? What would parents pay today if they just gave birth to a new baby and the child will attend college in 20 ​years?

Answer 1

Present Value:
PV = FV / (1+r)^n
Where r is Int rate per period
n - No. of periods

If Int Rate is 5.5%:

Particulars	Amount
Future Value	$            14,000.00
Int Rate	5.500%
Periods	20

Present Value = Future Value / ( 1 + r )^n
= $ 14000 / ( 1 + 0.055 ) ^ 20
= $ 14000 / ( 1.055 ) ^ 20
= $ 14000 / 2.9178
= $ 4798.21

Thus Amount to be deposited with university is $ 4798.21

If Int Rate is 3.5%:

Particulars	Amount
Future Value	$            14,000.00
Int Rate	3.500%
Periods	20

Present Value = Future Value / ( 1 + r )^n
= $ 14000 / ( 1 + 0.035 ) ^ 20
= $ 14000 / ( 1.035 ) ^ 20
= $ 14000 / 1.9898
= $ 7035.92
Thus Amount to be deposited with university is $ 7035.92