9. Use the nominal equivalent yield formula and demonstrate numerically for annual rates r1 0:01; 0:10;

9. Use the nominal equivalent yield formula and demonstrate numerically for annual

‘‘rates’’ r1 ¼ 0:01; 0:10; 0:25; 1:00, that as m ! y, the equivalent yield rmðr1Þ

gets closer and closer to lnð1 þ r1Þ. Consider m up to 1000, say. Show algebraically that if this limiting result is true for all r1, and n and rn are fixed, then as m ! y, the equivalent yield, rmðrnÞ, again gets closer and closer to lnð1 þ r1Þ where r1 is the annual rate equivalent to rn. (Note: These results can be proved with the tools of chapter 5, once the notion of the limit of a sequence is formally introduced, and chapter 9, which provides Taylor series approximations to the function ln x.)