Which expression is correct for the present value of an investment that is worth 9850 at the end of 6 years, if interest is paid at 3% per year, compounded quarterly? A) (9850)/((1.015)^12) B) (9850)/((1.03)^6) C) (9850)/((1.0075)^24) D) (9850)/((10025)^72)

The correct answer is C. Here's why:<br /><br />* **Understanding Present Value:** Present value is the current worth of a future sum of money, given a specified rate of return. It essentially discounts the future value back to the present.<br /><br />* **Compounding Periods:** The interest is compounded quarterly, meaning it's calculated four times a year. Over 6 years, this results in 6 * 4 = 24 compounding periods.<br /><br />* **Interest Rate per Period:** The annual interest rate is 3%, so the quarterly interest rate is 3%/4 = 0.75% or 0.0075 in decimal form.<br /><br />* **The Formula:** The formula for present value (PV) is:<br /><br /> PV = FV / (1 + r)^n<br /><br /> Where:<br /> * FV is the future value ($9850)<br /> * r is the interest rate per period (0.0075)<br /> * n is the number of periods (24)<br /><br />* **Calculation:** Plugging in the values, we get:<br /><br /> PV = 9850 / (1 + 0.0075)^24<br /><br /> PV = 9850 / (1.0075)^24<br /><br />Therefore, the correct expression for the present value is $\frac {9850}{(1.0075)^{24}}$.<br />