The price of a new car is $32,000. Assume that an individual makes a down payment of 25% toward the purchase of the car and secures financing for the balance at the rate of 7%/year compounded monthly. (Round your answers to the nearest cent.)
What will the interest charges be if she elects the 48-month plan? The 72-month plan?
To calculate the interest charges for each payment plan, we need to determine the loan amount for each plan and then calculate the interest charges using the given interest rate.
First, let's calculate the loan amount for each plan:
For the 48-month plan:
Down payment = 25% of $32,000 = $8,000
Loan amount = Price of the car - Down payment = $32,000 - $8,000 = $24,000
For the 72-month plan:
Down payment = 25% of $32,000 = $8,000
Loan amount = Price of the car - Down payment = $32,000 - $8,000 = $24,000
Now, let's calculate the interest charges for each plan using the given interest rate of 7%/year compounded monthly:
For the 48-month plan:
Number of months = 48
Monthly interest rate = Annual interest rate / 12 = 7% / 12 = 0.5833%
Interest charges = Loan amount * Monthly interest rate * Number of months
Interest charges = $24,000 * 0.5833% * 48 = $6,000
For the 72-month plan:
Number of months = 72
Monthly interest rate = Annual interest rate / 12 = 7% / 12 = 0.5833%
Interest charges = Loan amount * Monthly interest rate * Number of months
Interest charges = $24,000 * 0.5833% * 72 = $8,280
Therefore, the interest charges for the 48-month plan will be $6,000 and for the 72-month plan will be $8,280.
To calculate the interest charges for different financing plans, we need to find the loan amount and then calculate the total interest paid over the duration of the loan.
First, let's calculate the loan amount. Since the individual makes a 25% down payment, the loan amount will be the remaining 75% of the car's price:
Loan amount = $32,000 - (0.25 * $32,000) = $24,000
Next, let's calculate the interest charges for the 48-month plan. The interest rate is 7% per year, compounded monthly. We can use the formula for compound interest:
Interest = Principal * (1 + Rate/12)^n - Principal
Where:
Principal = Loan amount
Rate = Annual interest rate in decimal form
n = Number of compounding periods
For the 48-month plan:
Interest = $24,000 * (1 + 0.07/12)^(48*12) - $24,000
Calculating this using a calculator, the interest charges for the 48-month plan are approximately $4,493.33.
Now, let's calculate the interest charges for the 72-month plan:
For the 72-month plan:
Interest = $24,000 * (1 + 0.07/12)^(72*12) - $24,000
Calculating this, the interest charges for the 72-month plan are approximately $6,746.36.
Therefore, the interest charges for the 48-month plan are approximately $4,493.33, and for the 72-month plan are approximately $6,746.36.
Follow the same steps I just showed you here
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