You have just been offered a $1,000 par value bond for $847.88.The coupon rate is 8 percent,payable annually,and interest rates on new issues of the same degree of risk are 10 percent.You want to know how many more interest payments you will receive,but the party selling the bond cannot remember.Can you determine how many interest payments remain?
A) 14
B) 15
C) 12
D) 20
E) 10

Question

Quizplus · Accepted Answer

First, we need to calculate the annual interest payment of the bond using the coupon rate:

Annual Interest Payment = Coupon Rate x Par Value = 0.08 x $1,000 = $80

Next, we need to calculate the yield-to-maturity of the bond:

Yield-to-Maturity = Annual Interest Payment ÷ Current Bond Price + (Par Value - Current Bond Price) ÷ Years to Maturity

Using the given information, we can plug in the numbers:

10% = $80 ÷ $847.88 + ($1,000 - $847.88) ÷ Years to Maturity

Simplifying the equation:

10% = 0.0944 + 152.12 ÷ Years to Maturity

152.12 ÷ Years to Maturity = 0.056

Years to Maturity = 152.12 ÷ 0.056 = 2,717.14

Since we know that the bond pays interest annually, the remaining interest payments will be the number of years left until maturity rounded down to the nearest whole number.

Remaining Interest Payments = Floor(Years to Maturity) = 15

Therefore, the answer is B) 15.

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