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 $42,000 when the child reaches the age of 18? Assume the money earns 7% interest, compounded quarterly. (Round your answer to two decimal places.)
find P such that
P(1 + .07/4)^(4*18) = 42000
P(1.0175^72) = 42000
solve for P
To calculate the principal amount needed to reach $42,000 when the child reaches 18 years old, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value (in this case, $42,000)
P = the principal amount (what we want to find)
r = the interest rate (7% expressed as a decimal, so 0.07)
n = the number of times interest is compounded per year (quarterly, so 4)
t = the number of years (18)
Substituting the given values into the formula, we have:
$42,000 = P(1 + 0.07/4)^(4*18)
Now, let's solve for P:
P = $42,000 / (1 + 0.07/4)^(4*18)
P ≈ $6,733.57
Therefore, the couple must deposit approximately $6,733.57 when their child is born in order to have $42,000 when the child reaches the age of 18.
To find the principal amount that must be deposited by the parents when their child is born, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the future value (the desired amount when the child reaches 18)
P is the principal amount (the amount to be deposited)
r is the annual interest rate (7% or 0.07)
n is the number of times the interest is compounded per year (quarterly means 4 times per year)
t is the number of years (18 years)
We can plug in the given values:
42000 = P(1 + 0.07/4)^(4*18)
Now, we can solve for P using algebraic manipulation:
Divide both sides of the equation by (1 + 0.07/4)^(4*18):
42000 / (1 + 0.07/4)^(4*18) = P
Using a calculator or a computer, evaluate the right side of the equation:
42000 / (1 + 0.07/4)^(4*18) ≈ 7813.32
So, the principal amount that must be deposited by the parents when their child is born is approximately $7,813.32.