Let's break down and analyze this problem step-by-step.
1. Initial Cost of the Truck:
- John bought a used truck for \[tex]$4500.
2. Down Payment:
- He put down \$[/tex]1500 initially.
3. Monthly Payment:
- John agrees to make monthly payments of \$350 for the next 10 months.
4. Total Cost Paid:
- To find the total amount John paid for the truck, we need to add the down payment and the sum of all the monthly payments.
- The monthly payments for 10 months is: [tex]\(350 \times 10 = 3500\)[/tex]
- The total cost paid then is: [tex]\(1500 + 3500 = 5000\)[/tex]
5. Amount Financed:
- The amount financed (i.e., the amount John initially owes after the down payment) is the difference between the initial cost of the truck and the down payment.
- Amount financed = [tex]\(4500 - 1500 = 3000\)[/tex]
6. Total Interest Paid:
- The total interest paid is the difference between the total cost paid and the amount financed.
- Total interest paid = [tex]\(5000 - 3000 = 2000\)[/tex]
7. Monthly Interest Rate:
- We can calculate the monthly interest rate by seeing how much interest we are paying per month relative to the amount financed.
- Monthly interest rate = [tex]\(\frac{\text{Total interest paid}}{\text{Amount financed} \times \text{Number of months}}\)[/tex]
- Monthly interest rate = [tex]\(\frac{2000}{3000 \times 10} = \frac{2000}{30000} = \frac{2}{30} \approx 0.0667\)[/tex]
8. Yearly Rate of Interest:
- To find the annual interest rate, we multiply the monthly interest rate by 12 (since there are 12 months in a year) and then convert it to a percentage.
- Yearly interest rate = [tex]\(0.0667 \times 12 \times 100 = 80\%\)[/tex]
Thus, the effective yearly rate of interest for this deal is [tex]\(80\%\)[/tex].
Given the closest option to our calculated yearly interest rate from the provided choices, we should choose:
- [tex]\( \boxed{80\%} \)[/tex]
However, as none of the provided options match the calculated annual interest rate precisely, it appears there was a potential mistake or misprint within the provided options. Make sure to recheck your problem or provided options for any errors.
