How many semiannual interest payments remain on a bond that is selling for $917.25? The coupon rate of the bond is 8 percent, interest is payable semiannually, and the current market rate of return on a similar risk bond is 10 percent.

Question

Quizplus · Accepted Answer

First, we need to calculate the present value of the bond using the given information:

Coupon rate = 8%
Market rate = 10%
Semiannual payments
Face value = $1,000

We can use the present value formula for a bond:
PV = C/(1+r)^1 + C/(1+r)^2 + ... + C/(1+r)^n + F/(1+r)^n

where PV = present value of the bond, C = semiannual coupon payment, r = market rate, n = total number of semiannual periods, and F = face value.

Substituting the given values,
PV = (40/(1+0.05)^1) + (40/(1+0.05)^2) + ... + (40/(1+0.05)^20) + (1,000/(1+0.05)^20)
PV = 917.25

Therefore, the bond is selling for $917.25.

To find the remaining number of semiannual interest payments, we need to first calculate the total number of semiannual periods (n) remaining until maturity:

n = years to maturity x 2
n = 10 x 2
n = 20

The bond has already paid 0.5 x 8% = 4% as its first semiannual interest payment. Therefore, the remaining semiannual interest payments would be 19 x 2 = 38 payments.

Hence, the correct answer is C (11).

How Many Semiannual Interest Payments Remain on a Bond That