1. **State the problem:** We need to find the present value of an investment that will amount to $16,000 after 8 years with a nominal interest rate of 4.5% compounded monthly. 2. **Formula used:** The present value formula for compound interest is: $$ P = \frac{A}{\left(1 + \frac{r}{n}\right)^{nt}} $$ where: - $P$ is the present value (what we want to find), - $A$ is the amount after time $t$ (16,000), - $r$ is the nominal annual interest rate (4.5% or 0.045), - $n$ is the number of compounding periods per year (monthly means 12), - $t$ is the term in years (8). 3. **Substitute the values:** $$ P = \frac{16000}{\left(1 + \frac{0.045}{12}\right)^{12 \times 8}} $$ 4. **Calculate the base inside the parentheses:** $$ 1 + \frac{0.045}{12} = 1 + 0.00375 = 1.00375 $$ 5. **Calculate the exponent:** $$ 12 \times 8 = 96 $$ 6. **Calculate the denominator:** $$ 1.00375^{96} \approx 1.432364 $$ 7. **Calculate present value:** $$ P = \frac{16000}{1.432364} $$ 8. **Simplify the fraction:** $$ P = 11167.68 $$ 9. **Calculate compound interest:** $$ \text{Compound Interest} = A - P = 16000 - 11167.68 = 4832.32 $$ **Final answers:** - Present Value = $11167.68$ - Compound Interest = $4832.32$