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

Question

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:

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

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:

$$\boxed{{\displaystyle y=-225x+13500}}$$