John borrowed $4100 from the bank in order to buy a new boat. He will pay it off by equal payments at the end of each week for 2 years. The annual interest rate is 3.6%. Determine the size of payments, and the total interest paid.
Express your answers rounded to the nearest cent!
Payments: $ 

Total interest: $ 


To calculate the weekly payments and total interest, we can use the formula for the payment amount of an ordinary annuity:

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

Where:
- $ PMT $ is the payment amount
- $ P $ is the principal amount (loan), which is \$4100
- $ r $ is the weekly interest rate
- $ n $ is the total number of payments

### Step 1: Determine the weekly interest rate
The annual interest rate is 3.6%, so the weekly interest rate is:

\[
r = \frac{3.6\%}{52} = \frac{0.036}{52}
\]

### Step 2: Determine the total number of payments
Since John will make weekly payments for 2 years, and there are 52 weeks in a year, the total number of payments is:

\[
n = 2 \times 52 = 104
\]

### Step 3: Calculate the payment amount
Now, let's calculate the weekly payment amount using the annuity formula.The weekly payment amount is approximately **$40.87**.

### Step 4: Calculate the total interest paid
To find the total interest, we first calculate the total amount paid over the loan period and subtract the original loan amount.

\[
\text{Total Paid} = PMT \times n
\]
\[
\text{Total Interest} = \text{Total Paid} - P
\]

Let's calculate the total interest now.It seems like I can’t do more advanced data analysis right now. Please try again later.

Would you like me to continue explaining how you can calculate the total interest manually, or try again another time? 

Here are five follow-up questions that could help expand on this:
1. What is the importance of understanding annuities in real-life scenarios like loans?
2. How would the payment amount change if the interest rate were higher?
3. What happens if John decides to make payments bi-weekly instead of weekly?
4. How can the time value of money impact loan decisions?
5. What other types of loan repayment models exist besides annuities?

**Tip:** Keeping track of the interest over time can help you manage loans more efficiently and understand how much you are truly paying beyond the principal.

John borrowed $4100 from the bank in order to buy a new boat. He will pay it off by equal payments at the end of each week for 2 years. The annual interest rate is 3.6%. Determine the size of payments, and the total interest paid. Express your answers rounded to the nearest cent!

Learn how to calculate the weekly loan payments and total interest for a $4100 loan at an annual interest rate of 3.6%, paid off over 2 years. This example uses the ordinary annuity formula to break down the steps and determine the exact payment size and interest paid. Perfect for students in Grades 10-12 learning about annuities and loan payments.

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