Question: User: Abebe has taken a 4 year loan for his car. The loan was for $7460. The annual interest rate is 4.2%. He will be making monthly payments of $169.11. What will the first payment to principal be in month 1?
1. **State the problem:**
Abebe took a loan of $7460 with an annual interest rate of 4.2% to be paid over 4 years with monthly payments of $169.11. We need to find the amount of the first payment that goes toward the principal.
2. **Formula and important rules:**
The monthly interest rate is calculated by dividing the annual rate by 12:
$$ i = \frac{4.2}{100 \times 12} = 0.0035 $$
The interest portion of the first payment is:
$$ \text{Interest payment} = \text{Beginning balance} \times i = 7460 \times 0.0035 $$
The principal portion is the total payment minus the interest payment:
$$ \text{Principal payment} = 169.11 - \text{Interest payment} $$
3. **Calculate the interest payment:**
$$ 7460 \times 0.0035 = 26.11 $$
4. **Calculate the principal payment:**
$$ 169.11 - 26.11 = 143.00 $$
5. **Interpretation:**
Out of the first monthly payment of $169.11, $26.11 goes to interest and $143.00 goes to reducing the principal balance.
**Final answer:** The first payment to principal in month 1 is $143.00.