Question

What is the Macaulay duration of a 4-year annuity that makes annual payments of $1000 if the appropriate discount rate for this annuity is 8%, and the first payment is made exactly 1 year from today?

a) 4 years
b) 3.465 years
c) 3 years
d) 3.86 years

Answer 1

The Macaulay duration of a 4-year annuity with annual payments of $1000, a discount rate of 8%, and the first payment made 1 year from today is approximately 3.86 years.

Step-by-step explanation:

The Macaulay duration of a 4-year annuity can be calculated using the formula:

Macaulay duration = (∑(t * PV(t))) / ∑PV(t)

In this case, the annuity makes annual payments of $1000 for 4 years and the appropriate discount rate is 8%. We need to calculate the present value of each payment and multiply it by the corresponding time until payment, then sum up these values. Finally, divide the sum by the total present value of all payments.

Using this method, the Macaulay duration comes out to be approximately 3.86 years.