You decide to quit using your credit card and want to pay off the balance of $9,800 in 4 years. Your interest rate is 16.4% compounded monthly.

What will your monthly payments be?

$

How much interest do you pay?

$


To calculate the monthly payments and total interest paid, we will use the formula for the monthly payment of an amortizing loan:

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

Where:
- $M$ is the monthly payment.
- $P$ is the principal amount ($9,800).
- $r$ is the monthly interest rate (annual rate divided by 12).
- $n$ is the total number of payments (number of years multiplied by 12).

### Step 1: Calculate the monthly interest rate
The annual interest rate is 16.4%, so the monthly rate $r$ is:

\[
r = \frac{16.4\%}{12} = \frac{0.164}{12}
\]

### Step 2: Calculate the total number of payments
The total number of payments $n$ over 4 years is:

\[
n = 4 \times 12
\]

### Step 3: Calculate the monthly payment $M$
Using the formula with the values of $P$, $r$, and $n$, we will find $M$.

### Step 4: Calculate the total interest paid
The total interest paid is calculated as:

\[
\text{Total Interest} = (M \times n) - P
\]

Let’s calculate these values.### Results:
1. **Monthly Payment:** $279.75
2. **Total Interest Paid:** $3,627.83

You will pay $279.75 each month for 4 years, and over the life of the loan, you will pay a total of $3,627.83 in interest.

Would you like more details or have any questions?

Here are 5 related questions you might find useful:
1. How does changing the loan term affect the monthly payment?
2. What would the monthly payment be with a lower interest rate?
3. How much would you save in interest by making additional monthly payments?
4. What is the total amount paid at the end of the loan term?
5. How does compounding frequency (e.g., monthly vs. daily) affect the total interest?

**Tip:** Paying a little extra towards the principal each month can significantly reduce the total interest paid over the life of the loan.

You decide to quit using your credit card and want to pay off the balance of $9,800 in 4 years. Your interest rate is 16.4% compounded monthly. What will your monthly payments be? How much interest do you pay?

Learn how to calculate the monthly payments for paying off a $9,800 credit card balance with a 16.4% interest rate compounded monthly over 4 years. This example covers key finance concepts like amortization and compound interest, suitable for Grades 10-12.

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