Answer: $20,643.92
Explanation:
To calculate the future value of the certificate, we can use the formula:
FV = PV * (1 + r/n)^(n*t)
Where:
FV = future value
PV = present value (or initial investment)
r = annual interest rate (in decimal form)
n = number of compounding periods per year
t = number of years
In this case, we have:
PV = $8,000.00
r = 10% per year (or 0.10)
n = 4 (since interest is compounded quarterly)
t = 14 years
Plugging these values into the formula, we get:
FV = $8,000.00 * (1 + 0.10/4)^(4*14)
FV = $8,000.00 * (1 + 0.025)^56
FV = $8,000.00 * 2.58049
FV = $20,643.92
Therefore, the certificate will be worth $20,643.92 on Courtney's 17th birthday.