Question

Kita Ramin obtained a $3,000 loan to pay for a used car. She agreed to make 12 monthly payments of $266.22. What is the APR?

Answer 1

APR = 6.5%

Step-by-step explanation:

If Kita makes 12 payments of $266.22, the maturity value of the loan will be equal to:

V = 12 x $266.22 = $3194.64

On the other hand, the maturity value is equal to:

`V=P(1+r\cdot t)`

Where P is the initial amount, r is the Annual Percentage Rate APR and t is the time in years. So, replacing V by $3194.64, P by $3000, and t by 1 year (12 months), we get:

`\begin{gathered} 3194.64=3000(1+r\cdot1) \\ 3194.64=3000(1+r) \end{gathered}`

Now, we can solve for r as:

`\begin{gathered} (3194.64)/(3000)=(3000(1+r))/(3000) \\ 1.065=1+r \\ 1.065-1=1+r-1 \\ 0.065=r \end{gathered}`

So, the annual percentage rate is 0.065 or 6.5%