A woman borrows 

​$8000

at 

6​% 

compounded​ monthly, which is to be amortized over 3 years in equal monthly payments. For tax​ purposes, she needs to know the amount of interest paid during each year of the loan. Find the interest paid during the first​ year, the second​ year, and the third year of the 

loan. 

To solve this problem, we need to use the **amortization formula** to calculate the monthly payments, then calculate the interest paid in each year by analyzing the remaining balance over time.

### Step 1: Calculate the monthly payment

The formula for the monthly payment $ M $ is:

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

Where:
- $ P = 8000 $ is the loan amount.
- $ r = \frac{0.06}{12} = 0.005 $ is the monthly interest rate (annual rate divided by 12).
- $ n = 36 $ is the total number of payments (3 years = 36 months).

Let's calculate $ M $.

### Step 2: Break down the interest paid each year

Once we calculate the monthly payment $ M $, we can find the **interest portion** of each payment and the **principal repayment** by considering the outstanding loan balance at the beginning of each month.

- **First year**: 12 months
- **Second year**: 12 months
- **Third year**: Final 12 months

For each month, the interest is based on the remaining balance of the loan, which decreases as payments are made.

Let me calculate the monthly payment and interest paid in each year.The monthly payment is approximately **$243.38**.

### Step 3: Calculate the interest paid during each year

Next, I'll calculate the interest paid in each year by determining the interest portion of each monthly payment and the balance remaining over time.

Let’s proceed by calculating the interest paid in the first, second, and third years.The total interest paid during each year of the loan is as follows:

- **First year**: \$411.75
- **Second year**: \$257.02
- **Third year**: \$92.74

As the loan balance decreases over time, the amount of interest paid decreases while the principal repayment portion increases.

### Do you need more details or have any questions?

### 5 Related Questions:
1. How is the principal repayment calculated for each month?
2. What is the remaining loan balance at the end of the first year?
3. Can the same method be used for a different interest rate or loan term?
4. How do compounding frequencies affect the total interest paid?
5. What happens if the payments are not made monthly but biweekly or quarterly?

### Tip:
The faster you repay the principal, the less total interest you'll pay over the life of the loan.

A woman borrows $8000 at 6% compounded monthly, which is to be amortized over 3 years in equal monthly payments. For tax purposes, she needs to know the amount of interest paid during each year of the loan. Find the interest paid during the first year, the second year, and the third year of the loan.

Learn how to calculate the interest paid on a $8000 loan at 6% compounded monthly over 3 years. This problem covers amortization, loan repayment calculations, and how interest changes annually. Perfect for students in financial mathematics or personal finance studies.

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