To calculate how much a new parent should invest at 8% per year, compounded quarterly, to have $30,000 towards their children's college education in 15 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value (desired amount) of the investment
P = the principal amount (initial investment)
r = the annual interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the number of years
In this case:
A = $30,000
r = 8% = 0.08 (in decimal form)
n = 4 (quarterly compounding)
t = 15 years
Let's calculate the required principal amount (P):
$30,000 = P(1 + 0.08/4)^(4*15)
Simplifying the equation:
$30,000 = P(1.02)^(60)
Divide both sides by (1.02)^(60):
P = $30,000 / (1.02)^(60)
Using a calculator, compute (1.02)^(60) ≈ 2.2080403.
P ≈ $30,000 / 2.2080403
P ≈ $13,582.41
Therefore, the new parents should invest approximately $13,582.41 at 8% per year, compounded quarterly, to have $30,000 towards their children's college education in 15 years.