A car is purchased for $9,192.57 with $1470 down and a loan to be repaid at $200 a month for 2 years followed by a balloon payment. If the interest rate is 6% compounded monthly, how large will the balloon payment be?
To calculate the balloon payment, we need to first determine the loan amount.
The car was purchased for $9,192.57 with a down payment of $1470. Therefore, the loan amount is the difference between the purchase price and the down payment:
Loan amount = Purchase price - Down payment
Loan amount = $9,192.57 - $1470
Loan amount = $7,722.57
Next, we need to calculate the monthly interest rate. The interest rate is given as 6% per year, compounded monthly. To convert it into a monthly interest rate, we divide it by 12 months:
Monthly interest rate = Annual interest rate / 12
Monthly interest rate = 6% / 12
Monthly interest rate = 0.06 / 12
Monthly interest rate = 0.005
Now, we can calculate the balloon payment using the loan amount, monthly interest rate, and the number of months for repayment.
The loan is to be repaid over 2 years, which is a total of 24 months. The monthly payment is $200.
First, we need to calculate the accumulated value of the monthly payments over 24 months:
Accumulated value = Monthly payment * (1 - (1 + Monthly interest rate)^-Number of months) / Monthly interest rate
Accumulated value = $200 * (1 - (1 + 0.005)^-24) / 0.005
Using a calculator or spreadsheet, we find that the accumulated value of the monthly payments is approximately $4,600.62.
Finally, we can calculate the balloon payment:
Balloon payment = Loan amount - Accumulated value
Balloon payment = $7,722.57 - $4,600.62
Using a calculator or spreadsheet, we find that the balloon payment is approximately $3,121.95.
Therefore, the balloon payment for the car loan would be approximately $3,121.95.