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 300 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 % ​(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 must deposit "$74,806.25" today.

Step-by-step explanation:

The given values are:

Periodic payment,

P = $10,300

Rate of interest,

r =
`(4.4 \ percent)/(2)`

=
`2.2 \ percent`

Number of periods,

n =
`4* 2`

=
`8`

Now,

The PV of annuity will be:

=
`(P* [1 - (1 + r)^(-n)])/(r)`

On substituting the given values, we get

=
`(10,300* [1 - (1 + 2.2 \ percent)^(-8)])/(2.2 \ percent)`

=
`(1,645.73)/(2.2 \ percent)`

=
`74,806.25` ($)