Metlock Co$.$ accepts a note receivable from a customer in exchange for some damaged inventory. The note requires the customer

make semiannual installments of $$51,800$ each for $10$ years. The first installment begins $6$ months from the date the customer takes

delivery of the damaged inventory. Metlock's management estimates that the fair value of the damaged inventory is $$645,542.$

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$($a$1)$

What interest rate is Metlock implicitly charging the customer? Express the rate as an annual rate but assume semiannual

compounding. $($Round factor values to $5$ decimal places, e$.$g$.1\mathrm{.}25124$ and final answer to $0$ decimal places, e$.$g$.7\%.)$

The interest rate is

$\%$ annually.

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