Your grandfather is giving you an option to choose between two discount bonds. Both have the same coupon rate and required rate of return. However, one pays coupon annually and the other pays coupon semiannually. Which one would you choose?
If my grandfather is giving you an option to choose between two discount bonds and both have the same coupon rate and required rate of return. And if one pays coupon annually and the other pays coupon semiannually, then I will opt the bond that pays coupon semiannually as its effective yield to maturity will be greater than the bond pays coupon annually. Further, the cost/current price of the bond pays coupon semiannually will be comparatively low than the bond paying coupon annually.
So, Answer: I would choose the bond pays coupon semiannually.
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