Question

The semiannual tuition payment at a major university is expected to be $44,000 for the 4 years beginning 18 years from now. What lump sum payment should the university accept now, in lieu of tuition payments beginning 18 years, 6 months from now? Assume that money is worth 9%, compounded semiannually, and that tuition is paid at the end of each half-year for 4 years. (Round your answer to the nearest cent.)

Answer 1

The lump sum payment the university should accept now is approximately $225,133.41.

Step-by-step explanation:

To find the lump sum payment that the university should accept now, we can use the formula for the present value of an annuity. The semiannual tuition payment is $44,000 for 4 years, so the total number of payments is 8. The interest rate is 9% compounded semiannually. We need to find the present value of the annuity 18 years, 6 months from now.

The formula for the present value of an annuity is:

Present Value = Payment Amount * (1 - (1 + Interest Rate)^(-Number of Payments))) / Interest Rate

Plugging in the values, we get:

Present Value = $44,000 * (1 - (1 + 0.09/2)^(-8*2)) / (0.09/2)

Calculating this, we find that the lump sum payment the university should accept now is approximately $225,133.41.