An Insurance Company has a portfolio of two bonds:

$$ Bond $1$ is a bond with a Macaulay duration of $7\mathrm{.}28$ and a price of $35000$; and

$$ Bond $2$ is a bond with a Macaulay duration of $12\mathrm{.}74$ and a price of $65000.$

The price and Macaulay for both bonds were calculated using an annual effective interest

rate of $4\mathrm{.}32\%.$

Bailey estimates the value of this portfolio at an interest rate of i using the first$-$order

Macaulay approximation to be $105,000.$

Determine i