### CFA Practice Question

There are 490 practice questions for this study session.

### CFA Practice Question

A 10-year government zero coupon bond is currently yielding 6.4%. If in 10 years, you expect a two year government zero coupon bond to provide a yield of 10.7%, what must the yield be on a 12-year zero coupon bond today in order for you to be indifferent between the 10-year bond and the 12-year bond?
A. 7.1%
B. 7.7%
C. 8.4%
Explanation: To be indifferent, both securities must yield the same total dollar amount at the end of the investment horizon, which, in this case, is 12 years.

Option I: Buy a 10-year bond and then a two-year bond.
Option II: Buy a 12-year bond.

When indifferent: Option I = Option II
(1.064)10 (1.107) 2 = (1 + x) 12
= 7.1%
where x is the yield on the 12-year bond.

### User Contributed Comments12

User Comment
rgat why isn't the 10 yr and 12 yr forwards not divided by 2??
mountaingoat anyone help explain the logic behind the calculation: FV(10yr)*FV(2yr) = FV(12yr)?
ridone 6.4% is the yield in 10 of 12 years
and
10.7% is the yield in 2 of 12 years
hence
(6.4x10/12)+(10.7x2/12)=7.11%
jmelville rgat - I think you don't need to divide by 2 since it's a zero coupon bond
JeremyMartin i thought we should always assume that coupon rates are semiannual? when should we assume that rates are annual or semiannual?
YOUCANDOIT good question
danceadam The above answer is wrong. You should always use semi annual rates when valuing zero coupon bonds.
jfrank7 The answer is the same if you assume semi-annual payments and divide the interest rates by 2.
maria15 Ridone - I like your take on the calculation. Thanks!
birdperson jfrank7 - i disagree!

((1 + (.064/2))^20 * (1 +(.107/2))^4 ) ^ (1/12) - 1 = 7.237% not 7.1% which you get following the solution provided by analystnotes!
raywen8 ^ (1/24) instead of ^ (1/12)
ascruggs92 that was way easier than I thought