Final answer:
The price of a 3-year coupon bond with a face value of $1,000 and a coupon rate of 3.75% is $987.56.
Step-by-step explanation:
The price of a 3-year coupon bond with a face value of $1,000 and a coupon rate of 3.75% can be calculated using the present value formula. The coupon payment every year is $1,000 * 3.75% = $37.50. The market interest rate is 4.2%, which is greater than the bond's coupon rate. To calculate the bond's price, we need to find the present value of the future cash flows.
Using the formula:
Bond Price = Coupon Payment * (1 - (1 + Interest Rate)^(-Years)) / Interest Rate + Face Value * (1 + Interest Rate)^(-Years)
Substituting the given values:
Bond Price = $37.50 * (1 - (1 + 0.042)^(-3)) / 0.042 + $1,000 * (1 + 0.042)^(-3)
Bond Price = $987.56