If $500,000 of 10-year bonds with interest payable semiannually are sold for $494,040 based on
(1) the present value of $500,000 due in 20 periods at 5% plus
(2) the present value of twenty $25,000 payments at 5%, the nominal or contract rate and the market rate of interest for the bonds are both 10%.

Question

If $500,000 of 10-year bonds with interest payable semiannually are sold for $494,040 based on 
(1) the present value of $500,000 due in 20 periods at 5% plus 
(2) the present value of twenty $25,000 payments at 5%, the nominal or contract rate and the market rate of interest for the bonds are both 10%.

Quizplus · Accepted Answer

If the nominal or contract rate and the market rate of interest for the bonds are both 10%, then the bonds are issued at par (100% of face value). However, since the bonds were sold for $494,040 (less than face value), the effective interest rate must be higher than 10%. Therefore, (1) and (2) cannot both be true, and the statement is false.

If $500,000 of 10-Year Bonds with Interest Payable Semiannually Are