Questions: Suppose that you decide to borrow 17,000 for a new car. You can select one of the following loans, each requiring regular monthly payments. Installment Loan A: three-year loan at 5.1% Installment Loan B: five-year loan at 5.2% Use PMT = P(r/n) / [1 - (1 + r/n)^-nt] to complete parts (a) through (c) below. The total interest for Loan B is 2342.20. (Round to the nearest cent as needed.) c. Compare the monthly payments and the total interest for the two loans. Determine which loan is more economical. Choose the correct answer below. A. The five-year loan at 5.2% is more economical. B. The three-year loan at 5.1% is more economical. The buyer will save approximately in interest. (Round to the nearest cent as needed.)

Suppose that you decide to borrow 17,000 for a new car. You can select one of the following loans, each requiring regular monthly payments. Installment Loan A: three-year loan at 5.1% Installment Loan B: five-year loan at 5.2% Use PMT = P(r/n) / [1 - (1 + r/n)^-nt] to complete parts (a) through (c) below. The total interest for Loan B is 2342.20. (Round to the nearest cent as needed.) c. Compare the monthly payments and the total interest for the two loans. Determine which loan is more economical. Choose the correct answer below. A. The five-year loan at 5.2% is more economical. B. The three-year loan at 5.1% is more economical. The buyer will save approximately in interest. (Round to the nearest cent as needed.)
Transcript text: Suppose that you decide to borrow $\$ 17,000$ for a new car. You can select one of the following loans, each requiring regular monthly payments. Installment Loan A: three-year loan at 5.1\% Installment Loan B: five-year loan at 5.2\% Use PMT $=\frac{P\left(\frac{r}{n}\right)}{\left[1-\left(1+\frac{r}{n}\right)^{-n t}\right]}$ to complete parts (a) through (c) below. The total interest for Loan B is \$2342.20. (Round to the nearest cent as needed.) c. Compare the monthly payments and the total interest for the two loans. Determine which loan is more economical. Choose the correct answer below. A. The five-year loan at $5.2 \%$ is more economical. B. The three-year loan at $5.1 \%$ is more economical. The buyer will save approximately \$ $\square$ in interest. I (Round to the nearest cent as needed.)
failed

Solution

failed
failed

Solution Steps

Step 1: Convert the annual interest rate from a percentage to a decimal

To convert the annual interest rate to a decimal, divide by 100: \(r = 5.1 / 100 = 0.051\).

Step 2: Calculate the monthly interest rate

The monthly interest rate is calculated by dividing the annual interest rate by the number of payment periods per year: \(\frac{r}{n} = \frac{0.051}{12} = 0.00425\).

Step 3: Use the PMT formula to calculate the monthly payment

Using the PMT formula: \(PMT = \frac{P\left(\frac{r}{n}\right)}{\left[1-\left(1+\frac{r}{n}\right)^{-n t}\right]} = 510.27\).

Step 4: Calculate the total amount paid over the term of the loan

The total amount paid over the term of the loan is calculated by multiplying the monthly payment by the total number of payments: \(PMT \times n \times t = 18369.68\).

Step 5: Calculate the total interest paid

The total interest paid is the total amount paid over the term of the loan minus the principal amount: \(Total Paid - P = 18369.68 - 17000 = 1369.68\).

Final Answer:

The monthly payment is $510.27, and the total interest paid over the term of the loan is $1369.68.

Step 1: Convert the annual interest rate from a percentage to a decimal

To convert the annual interest rate to a decimal, divide by 100: \(r = 5.2 / 100 = 0.052\).

Step 2: Calculate the monthly interest rate

The monthly interest rate is calculated by dividing the annual interest rate by the number of payment periods per year: \(\frac{r}{n} = \frac{0.052}{12} = 0.00433\).

Step 3: Use the PMT formula to calculate the monthly payment

Using the PMT formula: \(PMT = \frac{P\left(\frac{r}{n}\right)}{\left[1-\left(1+\frac{r}{n}\right)^{-n t}\right]} = 322.37\).

Step 4: Calculate the total amount paid over the term of the loan

The total amount paid over the term of the loan is calculated by multiplying the monthly payment by the total number of payments: \(PMT \times n \times t = 19342.26\).

Step 5: Calculate the total interest paid

The total interest paid is the total amount paid over the term of the loan minus the principal amount: \(Total Paid - P = 19342.26 - 17000 = 2342.26\).

Final Answer:

The monthly payment is $322.37, and the total interest paid over the term of the loan is $2342.26.

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Which of the following pairs of numbers satisfies the equation 2x+3y=8? A x=1, y=2 B x=2, y=1 C x=-1, y=2 D x -> 2, y=4
failedAnswered
Divide using long division. State the quotient, q(x), and the remainder, r(x). (12 x^2 -7 x -3) ÷ (3 x -4) (12 x^2 -7 x -3) ÷ (3 x -4) =
failedAnswered
Quiz #4 (7.1-7.4) Question 19 of 30 This quiz: 30 point(s) poss This question: 1 point(s) How many times larger is a cubic meter than a cubic decimeter? A cubic meter is 1000 times larger than a cubic decimeter. (Type a whole number.)
failedAnswered
For the year ended December 31, Orion, Inc. mistakenly omitted adjusting entries for 1,500 of supplies that were used, (2) unearned revenue of 4,200 that was earned, and (3) insurance of 5,000 that expired. For the year ended December 31, what is the effect of these errors on revenues, expenses, and net income? a. Expenses are overstated by 6,500. b. Net income is overstated by 2,300. c. Expenses are understated by 3,500. d. Revenues are overstated by 4,200.
failedAnswered
Determine the domain on which the following function is increasing.