Question

1) 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 6.56.5 % on the deposited tuition, and a full refund will be available if the child chooses another university. The tuition is expected to be $18,000 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 4 %?

What would parents pay today if they just gave birth to a new baby and the child will attend college in 20 years?

2) The State of Confusion wants to change the current retirement policy for state employees. To do so, however, the state must pay the current pension fund members the present value of their promised future payments. There are 240,000 current employees in the state pension fund. The average employee is 20 years away from retirement, and the average promised future retirement benefit is $450,000 per employee. If the state has a discount rate of 6.5 % on all its funds, how much money will the state have to pay to the employees before it can start a new pension plan?

Answer 1

Note: In both the parts, it is assumed that the rate of return is compounded annually.

Part 1.

Amount to be paid today is the present value of the first year tuition fee ($18,000) calculated as follows:

(a) At the rate of return of 6.5%, amount to be paid (present value) is $5,108.35 as calculated below:

(b) At the interest rate of 4%, amount to be paid is $8,214.97 as follows:

Part 2:

Promised future retirement benefit per employee=$450,000

Present value of the promised benefit per employee = $127,708.66 as follows:

Total number of employees= 240,000

Therefore, total amount to be paid by the State= $127,708.66*240,000 = $30,650,079,123.51