Step 1 :Given that the loan required a total of 36 monthly payments of $314.76 each, we can calculate the total amount paid over the life of the loan by multiplying the monthly payment by the total number of payments. So, the total amount paid is \(314.76 \times 36 = 11331.36\).
Step 2 :The add-on interest rate was 4.6%, which means the original amount borrowed was the total amount paid divided by (1 + interest rate). So, the original amount borrowed is \(\frac{11331.36}{1 + 0.046} = 10833\).
Step 3 :Final Answer: The amount that Elon borrowed is \(\boxed{10833}\).