Question

a company offers a loan program with 0% interest on loans repaid within 5 years. A person took out a loan from this company and made equal monthly payments

After 6 monthly payments, the loan balance was $12,150
After 11 monthly payments, the loan balance was $11,025

which function can be used to find y, the balance of the loan after x monthly payments?


y=-225x+13500
y=225x-13500
y=-225x+13275
y=225x-13275

Answer 1

To determine the correct function for the loan balance \( y \) after \( x \) monthly payments, we can analyze the information given and create a linear equation.

1. After 6 payments, the balance is \( y = 12,150 \).
2. After 11 payments, the balance is \( y = 11,025 \).

First, we calculate the change in balance over the change in payments:

\[
\text{Change in balance} = 12,150 - 11,025 = 1,125
\]

\[
\text{Change in months} = 11 - 6 = 5
\]

Now we can determine the monthly payment amount:

\[
\text{Monthly payment} = \frac{1,125}{5} = 225
\]

So, the loan balance decreases by \( 225 \) for each month of payment.

Next, we can find the initial loan balance by recognizing that the balance after 6 payments is:

\[
y = \text{Initial balance} - 225 \times 6
\]
Let’s denote the initial balance as \( B \). Therefore:

\[
12,150 = B - 1,350 \quad \text{(since } 6 \times 225 = 1,350\text{)}
\]
\[
B = 12,150 + 1,350 = 13,500
\]

This means the initial loan balance is \( 13,500 \).

Now we will express \( y \) as a function of \( x \), the number of monthly payments:

\[
y = B - 225x
\]

Substituting \( B = 13,500 \),

\[
y = 13,500 - 225x
\]

This can be rewritten as:

\[
y = -225x + 13,500
\]

Now we can compare this function with the options given:

- \( y = -225x + 13500 \) (matches)
- \( y = 225x - 13500 \)
- \( y = -225x + 13275 \)
- \( y = 225x - 13275 \)

The correct function that can be used to find \( y \), the balance of the loan after \( x \) monthly payments, is:

\[
\boxed{y = -225x + 13500}
\]