Final answer:
To calculate the price you pay for the bond, determine the present value of its future cash flows using the formula for the present value of an annuity. The present value is calculated by dividing the coupon payment by the periodic interest rate and discounting it for the time it will take for each payment to be received.
Step-by-step explanation:
To calculate the price you would pay for the bond, you need to determine the present value of its future cash flows. Since the bond pays a 10% coupon semiannually, you can divide the coupon rate by 2 to find the periodic interest rate, which is 5%. There are 6 months between April 5th and the next coupon payment on July 1st. Using the formula for the present value of an annuity, you can calculate the present value of the bond's future cash flows:
Present Value = (Coupon Payment / (1 + r/2)^n) + (Coupon Payment / (1 + r/2)^(n+1)) + ... + (Coupon Payment + Face Value / (1 + r/2)^(n+m))
Plugging in the values, the present value of the bond would be:
Present Value = (50 / (1 + 0.05/2)^1) + (50 / (1 + 0.05/2)^2) + ... + (50 + 1000 / (1 + 0.05/2)^20)
You would then calculate the sum of these present values to find the price you would pay for the bond.