Kyle can buy a zero-coupon bond that will pay $1,600 at the end of 17 years and it is currently selling for 1,050. Instead he purchases a 8% bond with coupons payable quarterly that will pay $1,600 at the end of 13 years. If he pays x he will earn the same annual effective interest rate as the zero coupon bond.

Calculate x.

• $2,577.94
• $1,418.33
• $1,600.00
• $2,580.80
• $2,593.23

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

Solution: A

Suppose the quarterly yield rate on the zero coupon bond is [math]\mathrm{j}[/math].

Thus for the zero coupon bond [math]\mathrm{j}[/math] would equal:

[[math]] \begin{aligned} & 1,050=1600 \mathrm{v}^{68} \\ & \mathrm{v}^{68}=.65625 \\ & \mathrm{j}=.00621 \end{aligned} [[/math]]

Price of the coupon bond would be:

[[math]] \begin{aligned} & 1600 \mathrm{v}^{52}+1600(.02) \mathrm{a}_{\overline{52} | .00621} \\ & =2,577.94 \end{aligned} [[/math]]

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