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(Created page with "Joe must pay liabilities of 1,000 due 6 months from now and another 1,000 due one year from now. There are two available investments: Bond I: A 6-month bond with face amount of 1,000, an 8% nominal annual coupon rate convertible semiannually, and a 6% nominal annual yield rate convertible semiannually; Bond II: A one-year bond with face amount of 1,000, a 5% nominal annual coupon rate convertible semiannually, and a 7% nominal annual yield rate convertible semiannually...") |
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Calculate the amount of each bond that Joe should purchase to exactly match the liabilities. | Calculate the amount of each bond that Joe should purchase to exactly match the liabilities. | ||
<ul class="mw-excansopts"><li>Bond I | <ul class="mw-excansopts"><li>Bond I: 1, Bond II: 0.97561</li><li>Bond I: 0.93809, Bond II: 1</li><li>Bond I: 0.97561, Bond II: 0.94293</li><li>Bond I: 0.93809, Bond II: 0.97561</li><li>Bond I: 0.98345, Bond II: 0.97561</li></ul> | ||
{{soacopyright | 2023 }} | {{soacopyright | 2023 }} | ||
Revision as of 12:07, 1 October 2025
Joe must pay liabilities of 1,000 due 6 months from now and another 1,000 due one year from now. There are two available investments:
Bond I: A 6-month bond with face amount of 1,000, an 8% nominal annual coupon rate convertible semiannually, and a 6% nominal annual yield rate convertible semiannually;
Bond II: A one-year bond with face amount of 1,000, a 5% nominal annual coupon rate convertible semiannually, and a 7% nominal annual yield rate convertible semiannually.
Calculate the amount of each bond that Joe should purchase to exactly match the liabilities.
- Bond I: 1, Bond II: 0.97561
- Bond I: 0.93809, Bond II: 1
- Bond I: 0.97561, Bond II: 0.94293
- Bond I: 0.93809, Bond II: 0.97561
- Bond I: 0.98345, Bond II: 0.97561
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.