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Elon has misplaced the sales contract for his car and cannot remember the amount he originally financed. He does know that the add-on interest rate was $4.6 \%$ and the loan required a total of 36 monthly payments of $\$ 314.76$ each. How much did Elon borrow?
The amount that Elon borrowed is $\$ \square$. (Round to the nearest dollar as needed.)
Answer
Final Answer: The amount that Elon borrowed is \(\boxed{10833}\).
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 \(\boxed{10833}\).
