The price of a 36-year zero-coupon bond is 80% of its face value. A second bond, with the same price, same face value, and same annual effective yield rate, offers annual coupons with the coupon rate equal to 4 9 of the annual effective yield rate.

Calculate the number of years until maturity for the second bond.

• 45
• 54
• 63
• 72
• 81

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

Solution: D

Let i = yield rate, r = coupon rate (if any), F = face value, P = price, n = # of years. For the first bond:

[[math]] \begin{array}{l}{{P=0.8F=F_{V}{}^{36}}}\\ {{0.8=\nu^{36}}}\\ {{i=0.006218}}\end{array} [[/math]]

For the second bond:

[[math]] P=0.8F=F\nu^{n}+{\frac{4}{9}}(0.006218)F a_{n|0.006218} \\ 0.8 = v^n + (0.0027634)a_{n|0.006218} [[/math]]

Using the BAII Plus, where PV=0.8, I/Y=.6218, PMT=0.0027634, FV=1 CPT N results in n=72.

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