Under Logarithmic Interpolation,if He $t _ { i }$ -Tear Yield Is

Under logarithmic interpolation,if he $t _ { i }$ -tear yield is $y \left( t _ { i } \right)$ , $i = 1,2$ ,then the interpolated yield for $\pm$ lying between $t _ { 1 }$ and $t _ { 2 }$ is given by $y ( t ) = y \left( t _ { 1 } \right) \left[ 1 + \ln \left( 1 + x \cdot \left( t - t _ { 1 } \right) \right) \right],$ where $x$ is a parameter.Suppose the yield at one year is 4% and the yield at two years is 5%.Then,the closest yield at one and a half years,using logarithmic interpolation in time $t$ ,is

A) 4.47%
B) 4.50%
C) 4.53%
D) 4.55%

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