You want to buy a car. Suppose you borrow $15,000 for two years at an APR of 7%. What will your monthly payment be? How much interest will you have paid by the end of the loan?
I've gotten half of the question right, but I'm not sure which half since I can't only see that I have half a point on it.
I = PRT
I = 15,000 * 0.07 * 2
I = 2,100
(15,000 + 2,100) / 24 = ?
To calculate your monthly payment and the total interest paid on the loan, you need to use a loan repayment formula. Here's how you can do it step by step:
1. Convert the Annual Percentage Rate (APR) to a monthly interest rate: Divide the APR by 12 and then by 100. In this case, the monthly interest rate would be 7% divided by 12 (months) and then by 100: 0.07 / 12 = 0.00583.
2. Calculate the number of monthly payments: Since the loan term is for two years, there will be 24 monthly payments (2 years × 12 months per year).
3. Use the loan repayment formula: The formula to calculate the monthly payment on a loan is:
Monthly Payment = P × (r(1+r)^n) / ((1+r)^n - 1)
where:
- P is the principal amount (borrowed amount),
- r is the monthly interest rate, and
- n is the number of monthly payments.
Plugging in the values:
Monthly Payment = $15,000 × (0.00583(1+0.00583)^24) / ((1+0.00583)^24 - 1)
Note: You can use a calculator or spreadsheet software to perform this calculation easily.
4. Calculate the monthly payment amount: After performing the above calculation, you will find that the monthly payment on the loan is approximately $654.69.
5. Calculate the total interest paid: The total interest paid can be calculated by subtracting the principal amount from the total amount paid over the loan term. The total amount paid can be determined by multiplying the monthly payment by the number of months:
Total Interest = (Monthly Payment × Number of Months) - Principal Amount
Total Interest = ($654.69 × 24) - $15,000
After calculating this, you will find that the total interest paid on the loan would be approximately $5,913.56.
By following these steps, you'll be able to determine both the monthly payment and total interest paid on the loan.