Final answer:
The future value of $25,000 with a 7% interest compounded quarterly for 14 quarters is approximately $79,300.
Step-by-step explanation:
To calculate the future value of an investment with compound interest, we can use the formula:
FV = PV(1 + r/n)^(nt)
Where:
- FV is the future value
- PV is the present value (initial investment)
- r is the annual interest rate
- n is the number of times interest is compounded per year
- t is the number of years
In this case, we have:
PV = $25,000
r = 7%
n = 4 (quarterly compounding)
t = 14
Substituting these values into the formula:
FV = $25,000(1 + 0.07/4)^(4*14)
Simplifying and calculating:
FV = $25,000(1.0175)^56
FV ≈ $25,000 * 3.172
FV ≈ $79,300