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 800 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 4.5 % ​(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.)

Answer 1

You have to calculate the present value of the total of 8 six-monthly payments of $10,800 and it can be calculated with the help of PV of an Annuity formula

PV = PMT * [1-(1+i) ^-n)]/i

Where,

Present value (The money must you deposit today) (PV) =?

PMT = Six-monthly payment = $10,800

n = N = number of payments = 2 * 4 years = 8 payments

i = I/Y = interest rate per year =4.5 %; therefore six-monthly interest rate = 4.5%/2 = 2.25% per six-months

Therefore,

PV = $10,800* [1- (1+2.25%) ^-8]/2.25%

= $78,269.593751

Therefore today you have to deposit $78,269.593751 in the bank account so that you can make all the payments from this account and leaving the account empty when the last payment is made.