$i_1^{**}=7\mathrm{.}47\%,i_2^{**}=41\mathrm{.}35\%$The engineering design and testing group for Honda Motor Corp. does contract$-$based work for

automobile manufacturers throughout the world. During the last $3$ years, the net cash flows for

contract payments have varied widely, as shown below, primarily due to a large manufacturer's

inability to pay its contract fee.

$($a$)$ Determine the maximum number of $i^{**}$ values that may satisfy the ROR equation.

$($b$)$ Write the $PW$ equation and approximate the $i^{**}$ value$($s$)$ by plotting $PW$ vs $i.$