1. **State the problem:** We need to find the present value (PV) of an amount of 7663.95 given a nominal interest rate of 7.5% compounded semi-annually over 7 years. 2. **Formula used:** The present value formula for compound interest is: $$PV = \frac{FV}{\left(1 + \frac{r}{n}\right)^{nt}}$$ where: - $FV$ is the future value (7663.95), - $r$ is the nominal annual interest rate (7.5% or 0.075), - $n$ is the number of compounding periods per year (semi-annually means $n=2$), - $t$ is the time in years (7 years). 3. **Calculate the periodic interest rate:** $$\frac{r}{n} = \frac{0.075}{2} = 0.0375$$ 4. **Calculate the total number of compounding periods:** $$nt = 2 \times 7 = 14$$ 5. **Calculate the denominator:** $$\left(1 + 0.0375\right)^{14} = 1.0375^{14}$$ Using a calculator, $1.0375^{14} \approx 1.665832$ (rounded to six decimal places). 6. **Calculate the present value:** $$PV = \frac{7663.95}{1.665832} \approx 4600.00$$ **Final answer:** The present value is approximately **4600.00** rounded to the nearest cent.