Metlock Company purchased a machine at a price of $$100,000$ by signing a note payable, which requires a single payment of $$146,410$ in $4$ years.

$($a$)$

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Assuming annual compounding of interest, what rate of interest is being paid on the loan? Use either a financial calculator or the Excel function Rate to calculate the rate. $($Round answer to O decimal places, e$.$g $52\%).$

Rate of interest $\%$

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$($b$)$

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What would be the purchase price of the machine had Metlock negotiated a single payment of $$135,000$ in $4$ years, using the same effective rate? To calculate. use $(1)$ a financial calculator or $(2)$ Excel function PV$.($Round answer to $2$ decimol places eg$.5\mathrm{.}275\mathrm{.}25).$

Purchase price of the machine $

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