Final answer:
To calculate the dollar price of the bond, we need to discount the future cash flows from the bond to their present value.
Step-by-step explanation:
To calculate the dollar price of the bond, we need to discount the future cash flows from the bond to their present value. The coupon payments can be considered as an annuity, and the face value of the bond can be considered as a single payment at maturity. We can use the present value formulas for annuities and single payments to calculate the present value of each cash flow. Then, we sum up the present values to get the dollar price of the bond.
Using the given information: par value = $2,000, coupon rate = 5.1%, yield to maturity = 3.7%, and years to maturity = 14, we can calculate the present value of the coupon payments and the present value of the face value. Adding these two present values gives us the dollar price of the bond.
The formula for the present value of an annuity is: PV = C x [(1 - (1 + r)^-n) / r], where PV is the present value, C is the coupon payment, r is the yield to maturity divided by 2 (since the coupon is paid semiannually), and n is the number of coupon payments remaining (double the number of years to maturity).
The formula for the present value of a single payment is: PV = FV / (1 + r)^n, where PV is the present value, FV is the face value, r is the yield to maturity divided by 2 (since the coupon is paid semiannually), and n is the number of coupon payments remaining (double the number of years to maturity).
Using these formulas and the given information, we can calculate the present value of the coupon payments and the present value of the face value:
- The present value of the coupon payments is $__________ (calculated value).
- The present value of the face value is $__________ (calculated value).
Adding these two present values gives us the dollar price of the bond: $__________ (calculated value).