Question

Jane's daughter Sarah will start College in exactly16 years. The price of her target College is expected to be $32,000 every six months. This payment is due every six months beginning the day Sarah starts College, and since Sarah is expected to graduate after four years of College, will total 8 payments. Jane and her husband George currently have $14,000 saved for Sarah's College. They wish to begin a regular monthly savings program starting today and ending one month prior to Sarah beginning College. Assuming a rate of 8% compounded quarterly, how much will Jane and George have to save every month to achieve their financial College goals for Sarah?

(please detail for each step, thanks)

Answer 1

Rate if 8% compounded quarterly.

For every quarter, 8%/4 = 2% rate and for 6 months, the rate if (1.02*1.02)-1 = 4.04%

First, we find the PV of the educational payments at the start of Sarah's college (after 16 years)

Using a financial calculator

Set the calculator to BGN mode (2nd ==> PMT ==>2nd => ENTER)

FV = 0

I/Y = 4.04 (Rate of interest for 6 months)

N = 8 (8 semi-annual payments)

PMT = 32000

cpt PV, we get PV = 223782.16

Hence, the value of savings after 16 years should be $223782.16

Now, to calculate the monthly payment

PV = 14000

I/Y = 0.667 ( 8%/12 = 0.667% rate per month)

N = 191 (16 years*12 months -1 months = 191 months)

FV = -223782.16

cpt PMT, we get PMT = 450.47

Hence, the parents need to save $450.47 every month to reach their financial goal