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janelle wishes to finance a car for $33,000. the bank's annual interest rate is 3.5%, and she can choose between durations of five or six years. calculate the monthly payment and total amount paid for both duration options.

use the formula,
p = ar (1+r)^n/(1+r)^n-1
where a is the amount to finance, r is the monthly interest rate, and n is the number of months to pay. show all of your steps.

danny and sara interpret this insurance quote for their 2015 sports car and 2018 minivan.

determine the totals for items a, b, c, d, and e. show your work or explain how you got your answer.

(image is for the second question.)

1. 5 years — payment: $600.33; total repaid: $36,019.80

6 years — payment: $508.81; total repaid: $36,634.32

2. see below

Step-by-step explanation:

1.

First of all, the given formula cannot be used. It is missing parentheses around the denominator terms. We can add those, and we can simplify the formula so an exponential term only needs to be calculated once. An appropriate formula is ...

P = Ar/(1 -(1+r)^-n)

Naturally, the payment amount will be rounded to the nearest cent. The total of payments is ...

total paid = nP

Since you have more than one calculation to do, it is convenient to define the formula for a graphing calculator or spreadsheet and let the tool run the numbers. The result of doing that is shown in the attachment. The variable a₅ is used for the monthly payment amount for a 5-year loan; a₆ is the monthly payment for a 6-year loan.

In each case, the monthly interest rate is 3.5%/12, and the number of payments is 12 times the number of years.

(We are used to using P for the principal amount of the loan, and A for the amount of the monthly payment. That is why the variables "a" and "p" are swapped in the formula used in the attachment.)

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2.

Oddly enough, you find a total by adding up the quantities it is the total of.

a = $57.50 +49.50 +18.20 +38.90 +85.60 +2.00 +22.00 = $273.70

b = $59.10 +45.90 +18.20 +42.30 +90.80 +2.00 +22.00 = $280.30

c = a + 0 = $273.70

d = b + 76.10 = $356.40

e = c + d = $630.10

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"a" and "b" are subtotals that don't include Uninsured Motorist Bodily Injury. For the sports vehicle, that coverage was declined. For the minivan, the premium for that is added to the subtotal of "b" to get the minivan premium of "d".

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