a. ( 425)/((1+frac (0.09)(12))^24)

The expression represents a present value calculation. It's determining the amount of money needed today to have $425 in two years (24 months), assuming a 9% annual interest rate compounded monthly.<br /><br />Here's the breakdown and calculation:<br /><br />* **$425:** The future value (the amount you want to have in two years).<br />* **0.09:** The annual interest rate (9% expressed as a decimal).<br />* **0.09/12:** The monthly interest rate (annual rate divided by 12 months).<br />* **24:** The number of compounding periods (2 years * 12 months/year).<br />* **(1 + 0.09/12)^24:** The future value factor. This calculates how much $1 invested today will grow to in 24 months at the given interest rate.<br /><br />Calculation:<br /><br />1. **0.09 / 12 = 0.0075** (monthly interest rate)<br />2. **1 + 0.0075 = 1.0075**<br />3. **(1.0075)^24 ≈ 1.196413529**<br />4. **$425 / 1.196413529 ≈ $355.20**<br /><br />Therefore, the present value is approximately $\boxed{$355.20}$. This means you would need to invest approximately $355.20 today to have $425 in two years at a 9% annual interest rate compounded monthly.<br />