A couple plans to save for their child’s college education. What principal must be deposited by the parents when their child is born in order to have $100,000 when the child reaches age 18? Assume the money earns 4% interest, compounded quarterly.
p(1+.04/4)^(4*18) = 100000
p = 48849.61
To find the principal amount that needs to be deposited by the parents when their child is born, you need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the future value of the investment ($100,000 in this case)
P is the principal amount (what we need to find)
r is the annual interest rate (4% or 0.04 in decimal form)
n is the number of times the interest is compounded per year (quarterly compounding means n = 4, as there are 4 quarters in a year)
t is the number of years
In this case, the investment period is 18 years.
Plugging in the values we have into the formula, we get:
$100,000 = P(1 + 0.04/4)^(4*18)
Simplifying this equation, we need to solve for P.
First, let's simplify the exponent:
$(1 + 0.01)^(4*18)
Next, let's simplify the exponent further:
$(1.01)^72
Now, calculate the value of (1.01)^72:
(1.01)^72 = approximately 2.857263378
Now, our equation becomes:
$100,000 = P * 2.857263378
To find P, we can divide both sides of the equation by 2.857263378:
P = $100,000 / 2.857263378
P ≈ $34,927.04 (rounded to the nearest dollar)
Therefore, the couple needs to deposit approximately $34,927 when their child is born in order to have $100,000 when the child reaches 18 years of age.