Final answer:
To calculate the purchase price of the bond, use the present value formula. The bond has a face value of $2,500, a coupon rate of 3.20%, and is redeemable on July 1, 2021. The purchase price on February 10, 2015, is approximately $2,396.36.
Step-by-step explanation:
To calculate the purchase price of the bond, we need to use the present value formula. The present value of a bond is the discounted value of its future cash flows. In this case, the bond has a face value of $2,500, a coupon rate of 3.20%, and is redeemable on July 1, 2021.
First, we need to calculate the present value of the coupon payments. Since the coupon is paid semi-annually, there are 12 coupon payments (6 years * 2). Each coupon payment is $2,500 * 3.20% / 2 = $40. To calculate the present value of these cash flows, we need to discount each cash flow at the yield rate of 3.95% compounded semi-annually. Using the present value of an ordinary annuity formula, we can calculate the present value of the coupon payments.
Next, we need to calculate the present value of the face value payment. The face value payment occurs at the end of the bond's life and is also discounted at the yield rate of 3.95%. Using the present value of a single cash flow formula, we can calculate the present value of the face value payment.
Finally, we sum the present values of the coupon payments and the face value payment to get the purchase price of the bond. Rounding to the nearest cent, the purchase price on February 10, 2015, is approximately $2,396.36.