At the birth of a baby, a couple decides to make an initial investment of C at the rate of 7% compounded annually so that the amount will grow to $30,000 by her 10th birthday. What should their initial investment be? Round to the nearest dollars.
P = Po(1+r)^t = $30,000
Po(1+0.07)^10 = 30,000
Po = $15,251.
C * (1 + .07)^10 = 30000
The correct answer is 15,250.
To determine the initial investment required, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = final amount ($30,000)
P = principal (initial investment)
r = annual interest rate (7% as a decimal, which is 0.07)
n = number of times interest is compounded per year (since it's compounded annually, n = 1)
t = number of years (10 years)
We can rearrange the formula to solve for P:
P = A / (1 + r/n)^(nt)
Substituting the given values:
P = $30,000 / (1 + 0.07/1)^(1*10)
P = $30,000 / (1.07)^10
P ≈ $14,271.95
Therefore, the initial investment should be approximately $14,272.