-What is the duration of the municipal notes (the value of x)?
A)1.94 years.
B)2.00 years.
C)1.00 years.
D)1.81 years.
E)0.97 years.

Question

-What is the duration of the municipal notes (the value of x)?
A)1.94 years. 
B)2.00 years. 
C)1.00 years. 
D)1.81 years. 
E)0.97 years.

Quizplus · Accepted Answer

The duration of the municipal notes is the weighted average of the time until each payment is received. The weights are the present values of each payment divided by the present value of all payments. The present value of each payment is the payment multiplied by the discount factor for the time until the payment is received. The discount factor is the present value of $1 received at the end of the period, and is calculated as 1 / (1 + r)^t, where r is the annual interest rate and t is the time in years.In this case, the municipal notes have a face value of $1,000, a coupon rate of 5%, and a maturity of 2 years. The annual interest payment is $50, and the present value of the interest payments is $95.24. The present value of the principal payment is $905.73. The duration of the municipal notes is therefore:Duration = (95.24 * 1) + (905.73 * 2) / (95.24 + 905.73) = 1.94 years

-What Is the Duration of the Municipal Notes (The Value