Aerotron Electronics has just bought a used delivery truck for $$15,000.$ The small business paid $$1,000$ down and financed the rest,

with the agreement to pay nothing for the entire first year and then to pay $$506\mathrm{.}83$ at the end of each month over $2,3,$ and $4$

$($first payment is in $13$th month$).$

a$.$ What nominal interest rate is Aerotron paying on the loan?

$\%$

b$.$ What effective interest rate are they paying?

$\%$

Round your answer to $4$ decimal places for a and $b.$ The tolerance is $+-0\mathrm{.}0005.$

c$.$ How much of the $14$th month's payment is interest? How much is principal?

payment interest $=$$

$,$ and principal $=$$

d$.$ How much of the $18$th month's payment is interest? How much is principal?

payment interest $=$$

$,$ and principal $=$$

e$.$ How much of the $22$nd month's payment is interest? How much is principal?

payment interest $=$$

$,$ and principal $=$$

Round your answers to the nearest whole dollar for c$-$e$.$ The tolerance is $+-5.$