Question

Your son has been accepted into college. This college guarantees that your​ son's tuition will not increase for the four years he attends college. The first $11,000 tuition payment is due in six months. After​ that, the same payment is due every six months until you have made a total of eight payments. The college offers a bank account that allows you to withdraw money every six months and has a fixed APR of 6% (semiannual) guaranteed to remain the same over the next four years. How much money must you deposit today if you intend to make no further deposits and would like to make all the tuition payments from this​ account, leaving the account empty when the last payment is​ made?

Therefore the 6 % APR​ (semiannual) implies a semiannual discount rate of ____% ​(Round to one decimal​ places.)

Answer 1

- Periodic Semi-annual tution payment starting 6 months from now is $11,000

You will pay tution payment for 4 years every 6 months with a total of 8 payments. Tution payment during the 4 year payment period will remain same and will not increase.

Calculating the Present value of Tution payments today using PV of ordinary annuity formula:-

Where, C= Periodic Payments = $11,000

r = Periodic Interest rate = 6%/2 = 3%

n= no of periods = 4 years*2 = 8 (semiannual​ compounding)

Present value = $77,216.61

So, money must you deposit today is $77,216.61

- Therefore the 6 % APR​ (semiannual) implies a semiannual discount rate of 3.0% (6%/2)

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