A 27-year bond, with a price equal to 75% of its face value, offers annual coupons with the coupon rate equal to 21/37 of the annual effective yield rate. An n-year zero-coupon bond has the same price, face value, and yield rate.

Calculate n.

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• 9
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Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: C

[[math]] \begin{aligned} & 0.75 F=\frac{21}{37} i F a_{\overline{27}|i}+F v^{27} \\ & 0.75=\frac{21}{37}\left(1-v^{27}\right)+v^{27} \\ & 0.18243=\frac{16}{37} v^{27} \\ & i=0.03248 \\ & 0.75 F=F v^n \\ & (1+i)^n=\frac{4}{3} \\ & n=9\end{aligned} [[/math]]

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.