Final answer:
Using the compound interest formula, an investment of $750 at 7.5% interest compounded quarterly for 4.5 years will amount to approximately $1,492.14.
Step-by-step explanation:
To calculate the future value of an investment of $750 compounded quarterly at an interest rate of 7.5% for 4.5 years, we use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the amount of money accumulated after n years, including interest.
P = the principal amount ($750).
r = annual interest rate (decimal) (7.5% or 0.075).
n = number of times that interest is compounded per year (quarterly means n=4).
t = the time the money is invested for (4.5 years).
Plugging in the values, we get:
A = 750(1 + 0.075/4)^(4*4.5)
A = 750(1 + 0.01875)^(18)
A = 750(1.01875)^(18)
A ≈ 750 * 1.98951966
A ≈ $1,492.14
The investment will grow to approximately $1,492.14 after 4.5 years when compounded quarterly at 7.5%.