Revision as of 01:11, 20 November 2023 by Admin (Created page with "Graham is the beneficiary of an annuity due. At an annual effective interest rate of 5%, the present value of payments is 123,000 and the modified duration is <math>D_{MOD}</math>. Tyler uses the first-order Macaulay approximation to estimate the present value of Graham’s annuity due at an annual effective interest rate was 5.4%. Tyler estimates the present value to be 121,212. Calculate <math>D_{MOD}</math>, the modified duration of Graham’s annuity at 5%. <ul...")
Nov 20'23
Exercise
Graham is the beneficiary of an annuity due. At an annual effective interest rate of 5%, the present value of payments is 123,000 and the modified duration is [math]D_{MOD}[/math].
Tyler uses the first-order Macaulay approximation to estimate the present value of Graham’s annuity due at an annual effective interest rate was 5.4%. Tyler estimates the present value to be 121,212.
Calculate [math]D_{MOD}[/math], the modified duration of Graham’s annuity at 5%.
- 3.67
- 3.75
- 3.85
- 3.95
- 4.04
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
Nov 20'23
Solution: A
[[math]]
121,212=123,000\bigg(\frac{1.05}{1.054}\bigg)^{D_{MAC}}\Rightarrow D_{MAC}=\frac{\ln(121,212/123,000)}{\ln(1.05/1.054)}=3.851
[[/math]]
Then [math]D_{MOD} = 3.8512 /1.05 = 3.67[/math]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.