Alright, let's solve this step-by-step.
### Step 1: Calculate the total of payments
The given payments are [tex]$61.50, 261.00$[/tex], and [tex]$262.00$[/tex]. To find the total of these payments, we sum them up:
[tex]\[ \text{Total Payments} = 61.50 + 261.00 + 262.00 = 584.50 \][/tex]
### Step 2: Calculate the total interest [tex]\( c \)[/tex]
The total interest is found by subtracting the amount financed from the total payments:
[tex]\[ c = \text{Total Payments} - \text{Amount Financed} \][/tex]
Given [tex]\(\text{Amount Financed} = 3500 \)[/tex],
[tex]\[ c = 584.50 - 3500 = -2915.50 \][/tex]
### Step 3: Calculate the number of years
The problem states there are 12 payments per year. Given that we have 3 payments,
[tex]\[ \text{Number of Years} = \frac{\text{Number of Payments}}{\text{Payments per Year}} = \frac{3}{12} = 0.25 \][/tex]
### Step 4: Calculate the interest rate percent [tex]\( I \)[/tex]
To find the interest rate as a percentage, we use the formula:
[tex]\[ I = \left( \frac{c}{\text{Amount Financed}} \right) \times \frac{1}{\text{Number of Years}} \times 100 \][/tex]
Substitute [tex]\(c = -2915.50\)[/tex], [tex]\(\text{Amount Financed} = 3500\)[/tex], and [tex]\(\text{Number of Years} = 0.25\)[/tex]:
[tex]\[ I = \left( \frac{-2915.50}{3500} \right) \times \frac{1}{0.25} \times 100 \][/tex]
[tex]\[ I = -0.833 \times 4 \times 100 = -333.2 \][/tex]
### Final Answers
To the nearest penny, total interest [tex]\( c \)[/tex] is:
[tex]\[ c = -2915.50 \][/tex]
To the nearest tenth, the interest rate [tex]\( I \)[/tex] is:
[tex]\[ I = -333.2\% \][/tex]
