Question

What interest rate and length of loan would allow Keri to afford a $275 monthly car payment using the formula m = (12,000 + 12,000rt)/12t, where r represents the annual interest rate and t is the length of the loan in years? Provide an example to support your answer.

Answer 1

To find the interest rate and length of the loan, we can use the formula m = (12,000 + 12,000rt)/12t. Rearrange the equation to solve for r, and substitute the given values to find the interest rate and length of the loan. Example: Using a length of 5 years (t = 5), the interest rate (r) would be 4%, allowing Keri to afford the $275 monthly car payment.

Step-by-step explanation:

To find the interest rate and length of the loan that would allow Keri to afford a $275 monthly car payment using the formula m = (12,000 + 12,000rt)/12t, we need to solve for r and t.

1. Substitute the given values into the formula: $275 = (12,000 + 12,000r*t)/12t
2. Simplify the equation: 3,300t = 12,000 + 12,000rt
3. Rearrange the equation to isolate r: 12,000rt - 3,300t = 12,000
4. Factor out r: r(12,000t - 3,300) = 12,000
5. Divide both sides by (12,000t - 3,300) to solve for r: r = 12,000 / (12,000t - 3,300)

Example: If the length of the loan is 5 years (t = 5), the interest rate (r) would be r = 12,000 / (12,000*5 - 3,300), which equals 0.04 or 4%, meaning an annual interest rate of 4% would allow Keri to afford the $275 monthly car payment.