Question

You have been accepted into college. The college guarantees that your tuition will not increase for the four years you attend college. The first $ 10 comma 100 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 4.2 % ​(with semiannual​ compounding) 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? ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.)

The amount of money you must deposit today is $ _____ (round to nearest cent)

Answer 1

Tuition fee Total payments (n) (2 * 4) $ 10,000.00 8 (semi annual) Interest rate per annum Semi annual interest rate (4.2%/2 4.20% 2.10% Deposit required for all future tuition fees Present Value = $10,000 / 2.10% (1 - 1 / 1.02148) Present Value = $10,000 / 2.10% * (1 - 0.84683) Present Value = $10,000 / 2.10% * 0.15317 Present Value = $72,940.10 So the amount of money you must deposit today is $72,940.10