Question

A married couple is trying to finance their three-year-old son’s college education. Money can be deposited at 6% compounded quarterly. What end-of-quarter deposit must be made from the son’s 3rd birthday to his 18th birthday to provide $ 60,000 on each birthday from the 18th to the 21st? (Note that the first deposit comes three months after his 3rd birthday and the last deposit is made on the date of the first withdrawal.)

Answer 1

To provide $60,000 on each birthday from the 18th to the 21st, an end-of-quarter deposit of approximately $14,297.37 must be made.

Step-by-step explanation:

To calculate the end-of-quarter deposit that must be made to provide $60,000 on each of the son's birthdays from the 18th to the 21st, we can use the formula for compound interest:

A = P(1+r/n)^(nt)

Where:
A = future value ($60,000)
P = principal deposit (unknown)
r = annual interest rate (6% or 0.06)
n = number of compounding periods per year (4)
t = number of years (from the 3rd birthday to the 21st birthday, which is 18 years)

Let's solve for P:

$60,000 = P(1+0.06/4)^(4*18)

$60,000 = P(1.015)^72

$60,000/(1.015)^72 = P

P ≈ $14,297.37

The end-of-quarter deposit that must be made is approximately $14,297.37.

Answer 2

21-18=3 years of payments

Quarterly payments so= 3*12 payments

N=12

I=6/4=1.5

FV=$60,000

PV=0

PMT=?

Use financial calculator to compute PMT

You will need to contribute $4,600.80 at the end of each period to reach the future value of $60,000.00.

Step-by-step explanation: