Question

A father is now planing a savings program to put his daughter through college. She is 13, plans to enroll at the university in five years, and should graduate four years later. The annual cost is expected to be $15,000 when the daughter starts college, and is expected to remain the same for the four years when the daughter is in college. The college requires the payment at the start of each year. The father will make five equal annual deposits into the daughter's account starting one year from now. The account pays 6% annually.

Question 1

How much will the daughter need in her account when she starts college so that she will have just enough money to pay for her four years of college?

Question 2

How much must the father deposit in the daughter's account each of the next fie years so that the daughter will have just enough money to pay for her four years of college?

Please show full working on a piece of paper. Thanks

Answer 1

Dear Student

Please note the solution

Question 1

Start of year	Amount	PV @ 6%
1	15,000	= 15,000
2	15,000	= 15,000 / 1.06 = 14150.94
3	15,000	= 15,000 / 1.062 = 13349.95
4	15,000	= 15000 / 1.063 = 12594.29
		55,095.18

The amount requires at start of year $ 55,095.18 Answer.

Question 2

Father needs to deposit every year so that amount in the account stand at $ 55,095.18.

Let us assume father deposit, $ x amount every year, Then

     x * FVAF(r, n) = 55,095.18

=> x * FVAF(6%, 5) = 55,095.18

=> x * [ 1 + 1.06 + 1.06² + 1.06³ + 1.06⁴] = 55,095.18

=> x * 5.6371 = 55095.18

=> x = 55095.18 / 5.6371

         = $ 9,773.69 Answer

Father needs to deposit $ 9773.69 every year.