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 = $.
Accepted Solution
A:
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.