Question

Elon has misplaced the sales contract for his and cannot remember the amount he originally financed. He know that the add-on interest rate was 5.2% and the loan required a total of 36 monthly payments of $314.53 each. How much did Elon borrow?

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Answer to a math question Elon has misplaced the sales contract for his and cannot remember the amount he originally financed. He know that the add-on interest rate was 5.2% and the loan required a total of 36 monthly payments of $314.53 each. How much did Elon borrow?

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Hester

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To determine the amount Elon originally financed with an add-on interest rate, we can use the formula for calculating the principal in an add-on interest loan. The total repayment amount is the sum of the principal and the interest, which is spread out over the number of payments. The formula for the total repayment amount $ R $ in an add-on interest loan is: R = P + (P \times r \times t) Where: - $ P $ is the principal (the original amount borrowed), - $ r $ is the annual interest rate (as a decimal), - $ t $ is the loan term in years. Given: - Monthly payment $ M $ is $314.53, - Number of monthly payments $ n $ is 36, - Annual interest rate $ r $ is 5.2% or 0.052 as a decimal, - Loan term $ t $ is $ \frac{n}{12} $ years since there are 12 months in a year. The total repayment amount $ R $ is $ M \times n $. Now, we can set up the equation: R = P + (P \times 0.052 \times \frac{36}{12}) 314.53 \times 36 = P + (P \times 0.052 \times 3) Solving for $ P $: 11323.08 = P + (0.156 \times P)

11323.08 = P \times (1 + 0.156)

11323.08 = P \times 1.156

P = \frac{11323.08}{1.156}

P \approx 9790.03 So, Elon originally borrowed approximately 9790.03.

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