A $100,000 5-year 7% bond is issued on January 1, 2020. The bond pays interest annually. The market rate is 6%. What is the selling premium or discount on the bonds, rounded to nearest dollar?

Question

Quizplus · Accepted Answer

The bond will sell at a premium because its coupon rate (7%) is higher than the market rate (6%). To calculate the premium, we need to find the present value of the bond's cash flows (interest payments and principal repayment) discounted at the market rate (6%). The interest payment is $7,000 annually ($100,000 * 7%), and the principal repayment is $100,000 at the end of 5 years. Using the present value formula for an annuity and a single sum, the calculation is as follows:Present Value of Interest Payments = $7,000 * [(1 - (1 + 0.06)^-5) / 0.06] = $7,000 * 4.21236 ≈ $29,486Present Value of Principal Repayment = $100,000 / (1 + 0.06)^5 ≈ $74,733Total Present Value = $29,486 + $74,733 = $104,219The bond's selling price is $104,219, which is $4,219 above its face value. Rounding to the nearest dollar gives a premium of $4,213, making option B the correct answer.

A $100,000 5-Year 7% Bond Is Issued on January 1