Question

You have been accepted into college. The college guarantees that your tuition will not increase for the four years you attend. The first $10,000 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 4% (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

Answer 1

$73,254.81

Step-by-step explanation:

We assume fees paid as annuity (PMT). Now, we have to find Present Value (PV) of annuity

PV = PMT*(1- 1/(1+r)^n) / r

Where PMT = 10000, n = 8 payments, r r = ​4.0%/2 = 2% = 0.02

PV = $10,000 * (1 - 1/(1+0.02)^8) / 0.02

PV = $10,000 * (1 - 1/1.171659381) / 0.02

PV = $10,000 * 0.146509629 / 0.02

PV = $73254.8145

PV = $73,254.81

$73,254.81 is the money i must deposit today if i intend to make no further deposits and would like to make all the tuition payments from this account.