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

Multiple Choice

Under logarithmic interpolation, if he $t _ { i }$ -tear yield is $y \left( t _ { i } \right)$ , $i = 1,2$ , then the interpolated yield for $t$ 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%