A 20-year annual annuity with a yield of 7% has a duration of ________ years.Question 4Select one:a.11.33b.7.77c.15.14d.8.32
Question
A 20-year annual annuity with a yield of 7% has a duration of ________ years.
Question 4
Select one:
- a. 11.33
- b. 7.77
- c. 15.14
- d. 8.32
Solution
The duration of an annuity can be calculated using the formula for Macaulay Duration for an annuity:
D = (1 + r) / r - ( (1 + r - nr) / (r(1 + r)^(n-1)) )
where: D = duration r = yield or interest rate n = number of periods
In this case, r = 7% or 0.07 and n = 20 years.
Substituting these values into the formula:
D = (1 + 0.07) / 0.07 - ( (1 + 0.07 - 200.07) / (0.07(1 + 0.07)^(20-1)) )
Solving this equation will give you the duration of the annuity.
Please note that the calculation might be complex and you might need a calculator or software to solve it.
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