Flint Corp. was experiencing cash flow problems and was unable to pay its $$105,000$ account payable to Bramble Corp. when it fell due on September $30,2023.$ Bramble agreed to substitute a one$-$year note for the open account. The following two options were presented to Flint by Bramble:

Option $1$: A one$-$year note for $$105,000$ due September $30,2024.$ Interest at a rate of $8\%$ would be payable at maturity.

Option $2$: A one$-$year non$-$interest$-$bearing note for $$113,400.$ The implied rate of interest is $8\%.$

Assume that Bramble has a December $31$ year end.

$($a$)$