Questions: Question 15, 13.2.19 Part 1 of 2 HW Score: 20 -on method of calculating interest to find the total interest and the monthly payment. Points: 0 Amount of Loan 1300 Length of Loan 14 months Interest Rate 3.1% Add-on interest means that if a person borrows an amount P with an annual interest rate r and payments extended over t years, then the required interest comes from the simple interest formula I = Prt. Substitute the correct values into the formula and evaluate to find the total amount of interest. Be sure to convert the length of the loan into years before substituting it into the formula.

Calculate the total interest using the simple interest formula \( I = Prt \).

Identify the given values.

• Principal \( P = \$1300 \)
• Annual interest rate \( r = 3.1\% = 0.031 \)
• Length of loan \( t = 14 \) months

Convert the length of the loan from months to years.

Convert 14 months to years.

\( t = \frac{14}{12} = \frac{7}{6} \) years

Substitute the values into the simple interest formula \( I = Prt \).

Substitute \( P = 1300 \), \( r = 0.031 \), and \( t = \frac{7}{6} \).

\( I = 1300 \times 0.031 \times \frac{7}{6} \)

Calculate the total interest.

Perform the multiplication.

\( I = 1300 \times 0.031 \times \frac{7}{6} = 1300 \times 0.0361667 = 47.01667 \)

Round to the nearest cent.

\( I = \$47.02 \)

Calculate the monthly payment.

Add the total interest to the principal and divide by the number of months.

Total amount to repay \( = 1300 + 47.02 = 1347.02 \)

Monthly payment \( = \frac{1347.02}{14} = 96.2157 \)

Round to the nearest cent.

Monthly payment \( = \$96.22 \)

Total interest: \\(\boxed{I = \$47.02}\\)
Monthly payment: \\(\boxed{\text{Monthly Payment} = \$96.22}\\)