You want to buy a $21,000 car. The company is offering a 2% interest rate for 48 months (4 years). What will your monthly payments be?
To calculate the monthly payments on a car loan, we need to use the formula for calculating a fixed monthly payment:
Monthly Payment = (Principal Loan Amount * Monthly Interest Rate) / [1 - (1 + Monthly Interest Rate) ^ (-Number of Months)]
First, let's plug in the given information into the formula:
Principal Loan Amount (P) = $21,000
Annual Interest Rate (R) = 2% = 0.02 (decimal)
Number of Months (N) = 48 months
Since the interest rate is annual, we need to convert it to a monthly interest rate:
Monthly Interest Rate = Annual Interest Rate / 12
= 0.02 / 12
= 0.001666667
Now, we can plug the values into the formula:
Monthly Payment = (21,000 * 0.001666667) / [1 - (1 + 0.001666667) ^ (-48)]
Calculating the exponential term and performing the division:
Monthly Payment = (21,000 * 0.001666667) / [1 - 0.920925307028613]
= 34.99999867 / 0.07907469297138699
= 443.2131284
Rounding the monthly payment to two decimal places, the monthly payments for a $21,000 car loan with a 2% interest rate over 48 months would be approximately $443.21.