Treasury bonds paying an 8% coupon rate with semiannual payments currently sell at par value. What coupon rate would they have to pay in order to sell at par if they paid their coupons annually?
To find the coupon rate the bonds would have to pay in order to sell at par if they paid their coupons annually, we can use the concept of bond pricing. Bond prices are determined by the present value of future cash flows, where the cash flows include both the periodic coupon payments and the final par value payment at maturity.
In this case, we know that the Treasury bonds currently sell at par value (which means the price is equal to the face value or par value of the bond). We also know that the bonds currently pay an 8% coupon rate with semiannual payments.
To find the equivalent annual coupon rate, we need to convert the semiannual coupon payments to annual coupon payments. Since there are two coupon payments per year (semiannual), we can use the formula:
Annual Coupon Rate = Semiannual Coupon Rate * 2
In this case, the semiannual coupon rate is 8%, so the annual coupon rate would be:
Annual Coupon Rate = 8% * 2 = 16%
Therefore, the bonds would have to pay a 16% annual coupon rate in order to sell at par if they paid their coupons annually.