Amin buys a 24 year bond with a par value of $2,300 and annual coupons. The bond is redeemable at par. He pays $3,200 for the bond assuming an annual effective yield of i. the coupon rate is 4 times the yield rate. At the end of 9 years Amin sells the bond for S, which produces the same annual effective rate of I for the new buyer.

Calculate S.

• Insufficient information
• $3,051.19
• $3,721.43
• $1,875.37
• $2,156.91

Hardiek, Aaron (June 2010). "Study Questions for Actuarial Exam 2/FM". digitalcommons.calpoly.edu. Retrieved November 20, 2023.

Solution: B

[[math]] \mathrm{P}=3200 \quad \mathrm{~F}=\mathrm{C}=2300 [[/math]]

To calculate i:

[[math]] \begin{aligned} & 3200=2300 \mathrm{v}^{24}+2300(4 \mathrm{i}) \mathrm{a}_{\overline{24} |\mathrm{i}} \\ & 3200=2300 \mathrm{v}^{24}+9200\left(1-\mathrm{v}^{24}\right) \\ & -6000=\mathrm{v}^{24}-9200 \mathrm{v}^{24} \\ & \mathrm{i}=.0058 \\ & \mathrm{~s}=2300 \mathrm{v}^{15}+2300(4(.0058)) \mathrm{a}_{\overline{15}|.0058} \\ & =3,051.19 \end{aligned} [[/math]]

Hardiek, Aaron (June 2010). "Study Questions for Actuarial Exam 2/FM". digitalcommons.calpoly.edu. Retrieved November 20, 2023.