Question

The semiannual tuition payment at a major university is expected to be $37,000 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 5%, 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

Semi annual tuition payment beginning 18 years 6 months for four years = $37,000

Rate of interest = 5% compounded semi-annually = 2.5%

Further, number of periods = 4 years * 2 periods per year = 8 periods

So, this is an ordinary annuity of $37,000 @ 2.5% for 8 periods

Present value of this ordinary annuity at beginning of Year 18 = $37,000 * Present value interest factor for an annuity of $1 @ 2.5% for 8 periods

= $37,000 * 7.17013717 = $265,295.10

Now, Present value of this single sum at Year 18, with discounting @ 2.5% for 36 periods (18 years * 2 periods per year)

Present value interest factor for $1 @ 2.5% for 36 periods = 0.4111

So, present value now = $265,295.10 * 0.4111 = $109,062.80