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 $ 10 comma 000$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 %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

Answer:

The deposit will need to be in the order of $ 67,327,45

Explanation:

We are given the description of an annuity

we have a fixed amount of payment spread over time and we consider the time value of money (interest rate)

Therefore we sovle this, using the annuity present value formula:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 10,000.00

time 8

rate 0.04

$10000 \times \frac{1-(1+0.04)^{-8} }{0.04} = PV$

PV $67,327.4487