Questions: Suppose that you borrow 11,000 for three years at 6% toward the purchase of a car. Use PMT = P(r/n) / [1-(1+r/n)^(-nt)] to find the monthly payments and the total interest for the loan.
The monthly payment is
(Do not round until the final answer. Then round to the nearest cent as needed.)
The total interest for the loan is
(Use the answer from part (a) to find this answer. Round to the nearest cent as needed.)
Transcript text: Suppose that you borrow $\$ 11,000$ for three years at $6 \%$ toward the purchase of a car. Use PMT $=\frac{P\left(\frac{r}{n}\right)}{\left[1-\left(1+\frac{r}{n}\right)^{-n t}\right]}$ to find the monthly payments and the total interest for the loan.
The monthly payment is $\$$ $\square$
(Do not round until the final answer. Then round to the nearest cent as needed.)
The total interest for the loan is \$ $\square$
(Use the answer from part (a) to find this answer. Round to the nearest cent as needed.)
Solution
Solution Steps
Step 1: Convert the annual interest rate from a percentage to a decimal
The annual interest rate in decimal is 0.06.
Step 2: Calculate the monthly interest rate
The monthly interest rate is 0.005.
Step 3: Calculate the total number of payments
The total number of payments over the life of the loan is 36.
Step 4: Calculate the monthly payment using the PMT formula
The monthly payment, rounded to 2 decimal places, is $334.64.
Step 5: Calculate the total interest paid over the life of the loan
The total interest paid, rounded to 2 decimal places, is $1047.09.
Final Answer:
The monthly payment is $334.64 and the total interest paid over the life of the loan is $1047.09.