Question

1. if you buy a car for \\$8,000.00, have 36 months (installments) to pay it off. your interest rate is 0.05\\% (percent).

your insurance rate is \\$99.00 a month.

a.) what is your principal monthly payment?
b.) what is your total monthly payment when you add interest and insurance?

Explanation:

🆕 New Concept Discovered: Simple Interest and Installment Loans
Calculating monthly payments with interest and insurance

Step 1: Calculate principal monthly payment

The principal monthly payment is the total cost of the car divided by the number of months to pay it off, before adding any interest or insurance.

$$ \text{Principal Monthly Payment} = \frac{\$8,000.00}{36} \approx \$222.22 $$

Step 2: Calculate monthly interest

The interest rate is given as \(0.05\%\) (percent). In financial contexts for simple installment problems of this level, this rate is typically applied to the principal amount to find the total interest, or treated as a monthly rate. Assuming standard simple interest on the principal:

$$ \text{Total Interest} = \text{Principal} \times \text{Rate} \times \text{Time (in years)} $$

Convert 36 months to years:

$$ \text{Time} = \frac{36}{12} = 3\text{ years} $$

Convert the percentage rate to a decimal:

$$ 0.05\% = 0.0005 $$

Calculate total interest:

$$ \text{Total Interest} = \$8,000.00 \times 0.0005 \times 3 = \$12.00 $$

Calculate monthly interest payment:

$$ \text{Monthly Interest} = \frac{\$12.00}{36} \approx \$0.33 $$

Step 3: Calculate total monthly payment

Add the principal monthly payment, the monthly interest, and the monthly insurance rate together:

$$ \text{Total Monthly Payment} = \text{Principal Monthly Payment} + \text{Monthly Interest} + \text{Monthly Insurance} $$

$$ \text{Total Monthly Payment} = \$222.22 + \$0.33 + \$99.00 = \$321.55 $$

Answer:

a.) Principal monthly payment:
\( \$222.22 \)

b.) Total monthly payment:
\( \$321.55 \)