Question

Follow the steps above and find c, the total of the payments, and the monthly payment. Choose the right answers. Jane Smart buys a new SUV. The price, including tax, is $22,500.00. She finances the vehicle over 60 months after making a $2,000 down payment. The true annual interest rate is 12%. What are Jane's monthly payments (principal plus interest)? To the nearest penny, c = $. Total of payments = amount financed + c = $. Total of payments ÷ number of payments = monthly payment = $.

Answer 1

To calculate Jane's monthly car loan payments, we must determine the amount financed, total of the payments, and monthly payment. After deducting the down payment from the price of the SUV, we find the amount financed. To calculate the total of the payments, we multiply the amount financed by the monthly interest rate. Finally, we divide the total of the payments by the number of months to find the monthly payment.

Step-by-step explanation:

To find the monthly payments for Jane Smart's car loan, we need to calculate the amount financed, the total of the payments, and the monthly payment.

1. First, we calculate the amount financed by subtracting the down payment from the price of the SUV: $22,500 - $2,000 = $20,500.
2. Next, we calculate the total of the payments, which is the amount financed plus the interest. To calculate the interest, we multiply the amount financed by the true annual interest rate and divide by 12 to get the monthly interest rate: ($20,500 * 0.12) / 12 = $205.
3. Then, we add the amount financed to the total interest to get the total of the payments: $20,500 + $205 = $20,705.
4. Finally, we calculate the monthly payment by dividing the total of the payments by the number of months: $20,705 / 60 = $345.08 (rounded to the nearest penny).

So, Jane's monthly payment for the SUV is $345.08.

Answer 2

When the question is not clear, it is very important to state the assumptions.

Question says "true annual interest rate" = 12%. This seems to be equivalent to AER (annual equivalent rate) of 12%, and the monthly interest rate,
i = 1.12^(1/12)-1 = 0.948879% per month
With this interest rate, the monthly amount would be:
A=(P*(i*(1+i)^n))/((1+i)^n-1)
A=monthly payment
P=amount borrowed = 22500-2000=20500
i=0.948879% (per month)
n=60 months
=>
A=(P*(i*(1+i)^n))/((1+i)^n-1)
=(20500*(.00948879*(1+.00948879)^60))/((1+.00948879)^60-1)
=449.68
Total interest paid = 60*A-20500=6480.91


Question also says "Follow the steps above...", which we do not get to see, so there is another missing piece.

If it had been simple interest (very rate), then the monthly payment would be monthly payment=(22500-2000)*(1+0.12*5)/60=546.67.
This is over-estimated, because the full amount was not borrowed throughout the 5 years.

If the 12% given is the APR, which is twelve times the monthly interest, then the monthly payment would be calculated by the compound interest formula

A=(20500*(0.01*(1+0.01)^60))/((1+0.01)^60-1)
=456.01 (based on APR=12%, same assumption and results as zrh2sfo)
and the remaining calculations are the same as those of zrh2sfo.


NOTE: You can see that in math, it is best to post the original question, all parts completed, so we can see the actual problem. Helpers cannot help efficiently and correctly if only part of the question is posted, or worse, if there were typos. In the absence of information, helpers will have to make assumptions, which may or may not coincide with the intention of the question.