$30.$ Visteon, a spin$-$off company of Ford Motor Company, supplies major automobile components to auto manufacturers worldwide and is Ford's largest supplier. An engineer is on a Visteon committee to evaluate bids for new$-$generation coordinate$-$measuring machinery to be directly linked to the automated manufacturing of high$-$precision components. Three vendor bids include the interest rates. Visteon will make payments on a semi$-$annual basis only. The engineer is confused about the effective interest rates. What they are annually and over the payment period $($PP$)$ of $6-$months.

Bid $1$: $9\%$ per year, compounded quarterly

Bid $2$: $3\%$ per quarter, compounded quarterly

Bid $3$: $8\mathrm{.}8\%$ per year, compounded monthly

i$)$ Determine the effective rate for each bid on the basis of semi$-$annual payments, and construct cash flow diagrams for each bid rate.

ii$)$ What are the effective annual rates? These are to be a part of the final bid selection.

iii$)$ Which bid has the lowest effective annual rate?