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(Created page with "A bond has a modified duration of 8 and a price of 112,955 calculated using an annual effective interest rate of 6.4%. <math>E_{MAC}</math> is the estimated price of this bond at an interest rate of 7.0% using the first-order Macaulay approximation. <math>E_{MOD}</math> is the estimated price of this bond at an interest rate of 7.0% using the first-order modified approximation. Calculate <math>E_{MAC}-E_{MOD}</math>. <ul class="mw-excansopts"><li>91</li><li>102</li><li...") |
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SOA Life Insurance Life Insurance Company has a portfolio of two bonds: | |||
*Bond 1 is a bond with a Macaulay duration of 7.28 and a price of 35,000; and | |||
*Bond 2 is a bond with a Macaulay duration of 12.74 and a price of 65,000 | |||
<ul class="mw-excansopts"><li> | The price and Macaulay duration for both bonds were calculated using an annual effective | ||
interest rate of 4.32%. | |||
Bailey estimates the value of this portfolio at an interest rate of i using the first-order Macaulay | |||
approximation to be 105,000. | |||
Determine i. | |||
<ul class="mw-excansopts"><li>3.49%</li><li>3.62%</li><li>3.85%</li><li>3.92%</li><li>4.03%</li></ul> | |||
{{soacopyright | 2023 }} | {{soacopyright | 2023 }} | ||
Latest revision as of 13:17, 20 November 2023
SOA Life Insurance Life Insurance Company has a portfolio of two bonds:
- Bond 1 is a bond with a Macaulay duration of 7.28 and a price of 35,000; and
- Bond 2 is a bond with a Macaulay duration of 12.74 and a price of 65,000
The price and Macaulay duration for both bonds were calculated using an annual effective interest rate of 4.32%. Bailey estimates the value of this portfolio at an interest rate of i using the first-order Macaulay approximation to be 105,000.
Determine i.
- 3.49%
- 3.62%
- 3.85%
- 3.92%
- 4.03%
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.