What is the duration of an 8 percent annual payment two-year note that currently sells at par?
A)2 years.
B)1.75 years.
C)1.93 years.
D)1.5 years.
E)1.97 years.

Question

Quizplus · Accepted Answer

Since the note currently sells at par, this means its yield is equal to its coupon rate, which is 8%. Using the formula for the present value of an annuity, we can solve for the duration: 
PV = C x [1 - (1+r)^-n]/r 
Where PV is the present value (which is par in this case), C is the annual coupon payment, r is the annual interest rate (which is 8% in this case), and n is the duration of the note. 
Plug in the values: 
100 = 8 x [1 - (1+0.08)^-n]/0.08 
Simplify: 
12.5 = 1 - (1.08)^-n 
Multiply both sides by -1: 
-11.5 = (1.08)^-n 
Take the natural log of both sides: 
ln(-11.5) = -n x ln(1.08) 
Solve for n: 
n = ln(-11.5)/ln(1.08) ≈ 1.93 
Therefore, the duration of the note is approximately 1.93 years. The closest answer choice is C, 1.93 years.

What Is the Duration of an 8 Percent Annual Payment