A bond with the term of 20 years, face value of $5,000, a coupon rate of 8%, compounded quarterly and payments 4 times a year, was issued 15 years ago. Currently, interest rates are at 12%. What could the bond be sold for today?

Question

Quizplus · Accepted Answer

To find the current price of the bond, we use the present value formula for bonds, which accounts for the present value of the annuity (coupon payments) and the present value of the face value. The bond has 5 years left until maturity (20 - 15 = 5 years), with interest rates now at 12% and coupons paid quarterly. The coupon payment per period is (8% of $5,000) / 4 = $100. The number of periods is 5 years * 4 = 20 quarters. The market interest rate per period is 12% / 4 = 3%.The present value of the annuity (coupon payments) is calculated using the formula PV = P * [1 - (1 + r)^-n] / r, where P is the payment per period, r is the market interest rate per period, and n is the number of periods. Plugging in the values gives us the present value of the coupon payments.The present value of the face value is calculated using the formula PV = F / (1 + r)^n, where F is the face value.Adding these two present values gives the current price of the bond. Given the options, without doing the exact math, the correct answer is based on understanding that the bond's price will be below its face value because the market interest rate (12%) is higher than the coupon rate (8%). Among the given options, E ($4,256) is the only one that correctly reflects this situation.

A Bond with the Term of 20 Years, Face Value