Questions: Tobin borrowed 5000 from the bank in order to buy a new camper. He will pay it off by equal payments at the end of each week for 3 years. The annual interest rate is 5.6%. Determine the size of payments, and the total interest paid. Express your answers rounded to the nearest cent! Payments: Total interest:

Solution Steps

To determine the size of the weekly payments and the total interest paid, we can use the formula for the payment of an ordinary annuity. The formula for the payment \( P \) is given by:

\[ P = \frac{PV \cdot r}{1 - (1 + r)^{-n}} \]

where:

• \( PV \) is the present value of the loan (initial amount borrowed)
• \( r \) is the weekly interest rate
• \( n \) is the total number of payments

First, we need to convert the annual interest rate to a weekly interest rate and calculate the total number of weekly payments. Then, we can use the formula to find the weekly payment amount. Finally, we can calculate the total interest paid by subtracting the principal from the total amount paid over the term of the loan.

Given the annual interest rate of \(5.6\%\), we first convert it to a weekly interest rate. There are 52 weeks in a year, so the weekly interest rate \(r\) is calculated as:

\[ r = \frac{0.056}{52} \approx 0.001077 \]

The loan term is 3 years. Since there are 52 weeks in a year, the total number of weekly payments \(n\) is:

\[ n = 3 \times 52 = 156 \]

Using the formula for the payment of an ordinary annuity:

\[ P = \frac{PV \cdot r}{1 - (1 + r)^{-n}} \]

where \(PV = 5000\), \(r \approx 0.001077\), and \(n = 156\):

\[ P = \frac{5000 \times 0.001077}{1 - (1 + 0.001077)^{-156}} \approx 34.84 \]

The total amount paid over the term of the loan is the weekly payment multiplied by the total number of payments:

\[ \text{Total Amount Paid} = P \times n = 34.84 \times 156 \approx 5434.44 \]

The total interest paid is the total amount paid minus the principal:

\[ \text{Total Interest Paid} = 5434.44 - 5000 \approx 434.44 \]

Final Answer