The price of a new car is 20,000. Assume that an individual makes a down payment of 25% toward the purchase of a new car and secures financing for the balance at the rate of 10%/year compounded monthly.
What monthly payment will be required to make if the car is financed over a period of 36 months?
What will the interest be if she elects the 36-month plan?
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To find out the monthly payment required to finance the car over 36 months, we need to use the formula for calculating the monthly payment on a loan with compounded interest.
The formula for calculating the monthly payment is:
M = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
M = Monthly payment
P = Principal amount (remaining balance after down payment)
r = Monthly interest rate (annual interest rate divided by 12 and converted to decimal)
n = Total number of payments (36 months)
Let's calculate the monthly payment:
Step 1: Calculate the principal amount:
Principal amount = Price of the car - Down payment
Principal amount = $20,000 - (25% * $20,000)
Principal amount = $20,000 - $5,000
Principal amount = $15,000
Step 2: Calculate the monthly interest rate:
Monthly interest rate = (10% / 12) = 0.00833 (rounded to 5 decimal places)
Step 3: Calculate the monthly payment:
M = ($15,000 * 0.00833 * (1 + 0.00833)^36) / ((1 + 0.00833)^36 - 1)
Using a calculator, we can evaluate this expression and find that the monthly payment required to finance the car over 36 months is approximately $460.05.
Now, let's calculate the interest paid over the 36-month period:
Interest paid = (Monthly payment * Total number of payments) - Principal amount
Interest paid = ($460.05 * 36) - $15,000
Using a calculator, we can evaluate this expression and find that the interest paid over the 36-month period is approximately $744.20.