Find the APR (true annual interest rate), to the nearest $0.01 \%$, for the loan given below. $\begin{array}{cccc}\begin{array}{c}\text { Purchase } \\ \text { Price }\end{array} & \begin{array}{c}\text { Down } \\ \text { Payment }\end{array} & \begin{array}{c}\text { Add-On } \\ \text { Interest Rate }\end{array} & \begin{array}{c}\text { Number of } \\ \text { Payments }\end{array} \\ \$ 4150 & \$ 390 & 3.4 \% & 12\end{array}$ The APR for the loan amount is $\square \%$. (Type an integer or decimal rounded to the nearest hundredth as needed.)

Step 1 ：Given the purchase price of $4150, down payment of $390, add-on interest rate of 3.4%, and the number of payments is 12.

Step 2 ：First, calculate the loan amount, which is the purchase price minus the down payment. So, \(4150 - 390 = 3760\).

Step 3 ：Next, calculate the total interest paid over the life of the loan. This is done by multiplying the loan amount by the add-on interest rate. So, \(3760 \times 0.034 = 127.84\).

Step 4 ：Finally, calculate the APR using the formula: \(APR = \frac{2 \times n \times I}{P \times (n + 1)}\), where n is the number of payments, I is the total interest paid over the life of the loan, and P is the loan amount. Substituting the values, we get \(APR = \frac{2 \times 12 \times 127.84}{3760 \times (12 + 1)} = 6.28\%\).

Step 5 ：Final Answer: The APR for the loan amount is \(\boxed{6.28\%}\).