Part I:
The amount Kenneth has left to pay after receiving the cash back is:
$16,200 - $900 = $15,300
Part II:
The periodic rate at which Kenneth will be charged interest can be found using the formula:
r = (APR/12)/100
where APR is the annual percentage rate.
r = (4.56/12)/100
r = 0.0038
So the periodic rate is 0.0038 or 0.38%.
Part III:
To find Kenneth's monthly payment, we can use the formula for the present value of an annuity:
PMT = R * (PV * r) / (1 - (1 + r)^-n)
where PMT is the monthly payment, PV is the present value, r is the periodic interest rate, and n is the number of periods.
PV = $15,300
r = 0.0038
n = 36
R is the factor by which the payments change each period, but in this case, the payments are equal, so R is equal to 1.
PMT = 1 * ($15,300 * 0.0038) / (1 - (1 + 0.0038)^-36)
PMT = $451.66 (rounded to the nearest cent)
So Kenneth's monthly payment is $451.66.
Part IV:
If Kenneth hadn't received the cash back, his present value would have been $16,200, so we can use the same formula as before to find his monthly payment:
PV = $16,200
r = 0.0038
n = 36
PMT = 1 * ($16,200 * 0.0038) / (1 - (1 + 0.0038)^-36)
PMT = $478.59 (rounded to the nearest cent)
So Kenneth's monthly payment would have been $478.59.
Part V:
To find out how much money Kenneth saved by receiving the cash back, we can subtract his monthly payment with the cash back from his monthly payment without the cash back:
$478.59 - $451.66 = $26.93 (rounded to the nearest cent)
So Kenneth saved $26.93 per month, or a total of:
$26.93 * 36 = $968.28
Therefore, Kenneth saved $968.28 by receiving the cash back.