The interest rate is 7 percent per year.Compute the eight-month zero-coupon bond price using a compound interest rate with monthly compounding.

Question

Quizplus · Accepted Answer

The first step is to convert the annual interest rate to a monthly rate:
r = 7% / 12 = 0.5833% per month
The time to maturity of the bond is 8/12 = 0.67 years, or 8 months.
Using the formula for the present value of a zero-coupon bond:
P = FV / (1+r)^n
where P is the bond price, FV is the face value of the bond (which is usually $1000 but is not given in this problem), r is the monthly interest rate, and n is the number of months to maturity.
Substituting the values given in the problem:
P = FV / (1+0.5833%)^8
P = FV / 1.0482
P = 0.9535 * FV
Therefore, the answer is closest to choice C, $0.9545.

The Interest Rate Is 7 Percent Per Year