You have just been offered a $1,000 par value bond for $847.88. The coupon rate is 8 percent, payable annually, and annual interest rates on new issues of the same degree of risk are 10 percent. You want to know how many more interest pay¬ments you will receive, but the party selling the bond cannot remember. Can you determine how many interest payments remain?

Question

Quizplus · Accepted Answer

First, calculate the annual interest payment: 
Coupon rate x Par value = Annual interest payment 
0.08 x $1,000 = $80

Next, calculate the yield to maturity: 
Market price = Present value of future cash flows 
$847.88 = $80 / (1 + y)^1 + $80 / (1 + y)^2 + … + $80 / (1 + y)^n + $1,000 / (1 + y)^n 
Where n is the number of interest payments remaining.

Using a financial calculator or Excel, the yield to maturity can be calculated as 9.43%.

Then, use the yield to maturity to calculate the number of interest payments remaining: 
n = log[(Par value / Market price + Annual interest payment) / Annual interest payment] / log(1 + Yield to maturity) 
n = log[(1,000 / 847.88 + 80) / 80] / log(1 + 0.0943) 
n ≈ 15

Therefore, there are 15 interest payments remaining.

You Have Just Been Offered a $1,000 Par Value Bond