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# Since the bonds have a facevalue of1000and

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Unformatted text preview: + [(\$100,000 0%) Present Value of an Ordinary Annuity Factor] PV factor \$35,056 ÷ \$100,000 .35056 Examining Table 4 in Appendix A (i.e., present value of \$1 table) for n = 8, we find that the effective rate is 14%. E11–25 Concluded Note 3 \$922 = (\$1,000 Present Value Factor) + [(\$1,000 7%) Present Value of an Ordinary Annuity Factor] Since the proceeds (i.e., present value) are less than the face value, we know that the note was issued at a discount. Consequently, the effective rate must be more than the stated rate. Try i = 9% for n = 5: (\$1,000 .64993 from Table 4 in Appendix A) + [(\$1,000 7%) 3.88965 from Table 5 in Appendix A)] = \$649.93 + \$272.28 = \$922 (rounded) Therefore, the annual effective interest rate must be 9%. Bond 1 \$11,635 = (\$10,000 Present Value Factor) + [(\$10,000 3%) Present Value of an Ordinary Annuity Factor] Since the proceeds are greater than the face value, we know that the bond was issued at a premium. Consequently, the effective rate is less than the stated rate. Try i = 2% for n = 20: (\$10,000 .67297 from Table 4 in Appendix A) + [(\$10,000 3%) 16.35143 from Table 5 in Appendix A] = \$6,729.70 + \$4,905.43 = \$11,635 (rounded) The effective rate per period is 2%. Since there are two interest periods per year, the annual effective interest rate is 4%. Bond 2 \$54,323 = (\$50,000 Present Value Factor) + [(\$50,000 4.5%) Present Value of an Ordinary Annuity Factor] Since the proceeds (i.e., present value) are greater than the face value, we know that the bond was issued at a premium. Consequently, the effective rate must be less than the stated rate. Try i = 4% for n = 30: (\$50,000 .30832 from Table 4 in Appendix A) + [(\$50,000 4.5%) 17.29203 from Table 5 in Appendix A] = \$15,416.00 + \$38,907.07 = \$54,323 (rounded) The effective rate per period is 4%. Since there are two interest periods per year, the annual effective interest rate is 8%. E11–26 a. Since the bonds have a face value of \$1,000 and they are selling for 89.16, an individual bond would have a present value of \$891.60 (\$1,000 x 89.16%). For these bonds to be attractive to an investor who requires an annual rate of return of 12%, the present value of the bonds' future cash flo...
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