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(Created page with "'''Key: C''' Let P be the premium after the July 1, CY3 rate change. On November 15, CY5 the premium is 0.96P and on October 1, CY6 it becomes 1.05(0.96)P = 1.008P. The relev...") |
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Let P be the premium after the July 1, CY3 rate change. On November 15, CY5 the premium is 0.96P and on October 1, CY6 it becomes 1.05(0.96)P = 1.008P. The relevant parallelogram is: | Let P be the premium after the July 1, CY3 rate change. On November 15, CY5 the premium is 0.96P and on October 1, CY6 it becomes 1.05(0.96)P = 1.008P. The relevant parallelogram is: | ||
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{{#invoke_html:actuarial_science/pgram|html|700|300|70|4|7/1/3|11/15/5|10/1/6|7|-4|5}} | {{#invoke_html:actuarial_science/pgram|html|700|300|70|4|7/1/3|11/15/5|10/1/6|7|-4|5}} | ||
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The upper left triangle for CY6 has area (1/2)(7/8)2 = 49/128 and the lower right triangle has area (1/2)(1/4)2 = 4/128. The weighted average is [49 + 4(1.008) + 75(0.960)]P/128 = 0.9768P. The current premium is 9200(1.008)/(0.9768) = 9494. | The upper left triangle for CY6 has area (1/2)(7/8)2 = 49/128 and the lower right triangle has area (1/2)(1/4)2 = 4/128. The weighted average is [49 + 4(1.008) + 75(0.960)]P/128 = 0.9768P. The current premium is 9200(1.008)/(0.9768) = 9494. | ||
{{soacopyright | 2023}} | {{soacopyright | 2023}} |
Revision as of 21:09, 15 May 2023
Key: C
Let P be the premium after the July 1, CY3 rate change. On November 15, CY5 the premium is 0.96P and on October 1, CY6 it becomes 1.05(0.96)P = 1.008P. The relevant parallelogram is:
The upper left triangle for CY6 has area (1/2)(7/8)2 = 49/128 and the lower right triangle has area (1/2)(1/4)2 = 4/128. The weighted average is [49 + 4(1.008) + 75(0.960)]P/128 = 0.9768P. The current premium is 9200(1.008)/(0.9768) = 9494.