Andrew construction borrows the entire cost of a new dump truck. The loan has an annual interest rate of 12 percent and calls for monthly payments of $1,000 over a five-year period. What is the cost of the truck?
To find the cost of the truck, we first need to determine the total amount paid over the five-year period for the loan. We can then subtract the total interest paid from that amount to get the cost of the truck.
The loan has an annual interest rate of 12 percent, which needs to be converted to a monthly interest rate. Since there are 12 months in a year, we divide the annual interest rate by 12 to get the monthly interest rate.
Monthly interest rate = Annual interest rate / 12 = 12% / 12 = 1% = 0.01
Now, we can calculate the total amount paid over the five-year period by multiplying the monthly payment by the total number of months.
Total months = 5 years * 12 months/year = 60 months
Total amount paid = Monthly payment * Total months = $1,000 * 60 = $60,000
Next, we need to calculate the total interest paid over the five-year period. To do this, we multiply the outstanding loan balance by the monthly interest rate for each month and sum up these amounts.
Since the loan balance decreases each month as payments are made, we can use the amortization method to calculate the interest paid for each month.
First, let's find the loan balance at the beginning. Since Andrew borrowed the entire cost of the truck, the loan balance at the beginning is equal to the cost of the truck.
Loan balance at the beginning = Cost of the truck
Next, we calculate the monthly interest payment for each month using the loan balance at the beginning and the monthly interest rate.
Monthly interest payment = Loan balance at the beginning * Monthly interest rate
Then, we subtract the monthly interest payment from the monthly payment to find the amount of principal paid for each month.
Principal payment = Monthly payment - Monthly interest payment
Finally, we subtract the principal payment from the loan balance at the beginning to get the new loan balance for the next month.
New loan balance = Loan balance at the beginning - Principal payment
By repeating these steps for each month, we can calculate the total interest paid over the five-year period.
Once we have the total interest paid, we can subtract it from the total amount paid to find the cost of the truck.
Cost of the truck = Total amount paid - Total interest paid.