question 7 of 8 attempt 3 when interest rates are low, some automobile dealers offer loans at 0% apr, as indicated in a 2021 advertisement by a prominent car dealership, offering zero percent financing or cash back deals on some models. zero percent financing means the obvious thing - that no interest is being charged on the loan. so if we borrow $1200 at 0% interest and pay it off over 12 months, our monthly payment will be $\frac{1200}{12} = $100. suppose you are buying a new truck at a price of $20,000. you plan to finance your purchase with a loan that you will repay over two years. the dealer offers two options: either dealer financing with 0% interest, or a $2000 rebate on the purchase price. if you take the rebate, you will have to go to the local bank for a loan (of $18,000) at an apr of 6.5%. should you take the dealer financing or the rebate? dealer financing rebate there is not enough information to make a decision. how much would you save over the life of the loan by taking the option you chose? (round your answer to the nearest cent.) you would save $ over the life of the loan.

Question

question 7 of 8 > attempt 3 when interest rates are low, some automobile dealers offer loans at 0% apr, as indicated in a 2021 advertisement by a prominent car dealership, offering zero percent financing or cash back deals on some models. zero percent financing means the obvious thing - that no interest is being charged on the loan. so if we borrow $1200 at 0% interest and pay it off over 12 months, our monthly payment will be $\frac{1200}{12} = $100. suppose you are buying a new truck at a price of $20,000. you plan to finance your purchase with a loan that you will repay over two years. the dealer offers two options: either dealer financing with 0% interest, or a $2000 rebate on the purchase price. if you take the rebate, you will have to go to the local bank for a loan (of $18,000) at an apr of 6.5%. should you take the dealer financing or the rebate? dealer financing rebate there is not enough information to make a decision. how much would you save over the life of the loan by taking the option you chose? (round your answer to the nearest cent.) you would save $ over the life of the loan.

Accepted Answer

# Explanation:
## Step1: Calculate total payment with dealer financing
The truck price is $20000$ and with dealer - financing at 0% interest for 2 years (24 months), the total amount paid is the purchase price, so the total payment $P_1 = 20000$.
## Step2: Calculate monthly payment with bank loan (after rebate)
The loan amount $L=18000$, the annual percentage rate $APR = 6.5\%=0.065$, so the monthly interest rate $r=\frac{0.065}{12}$. The number of payments $n = 24$.
The formula for the monthly payment of a loan is $M=\frac{L\times r\times(1 + r)^n}{(1 + r)^n-1}$.
Substitute the values:
$$
\begin{align*}
r&=\frac{0.065}{12}\approx0.005417\
M&=\frac{18000\times0.005417\times(1 + 0.005417)^{24}}{(1 + 0.005417)^{24}-1}\
(1 + 0.005417)^{24}&\approx1.1327\
M&=\frac{18000\times0.005417\times1.1327}{1.1327 - 1}\
&=\frac{18000\times0.005417\times1.1327}{0.1327}\
&=\frac{18000\times0.00613}{0.1327}\
&=\frac{110.34}{0.1327}\
&\approx831.5
\end{align*}
$$
The total amount paid with the bank - loan (after rebate) is $P_2 = M\times n=831.5\times24 = 19956$.
## Step3: Calculate the savings
The savings $S=P_1 - P_2=20000 - 19956 = 44$.

# Answer:
Rebate
You would save $44.00$

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Question

Explanation:

Step1: Calculate total payment with dealer financing

Step2: Calculate monthly payment with bank loan (after rebate)

Step3: Calculate the savings

Answer: