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A loan of $13,500 is made at an effective interest rate of 9.5%. Payments are made at the end of each interest period. Each payment equals twice the interest due until the borrower pays off the outstanding debt with a final payment of, at most, $1,800. Find the number of payments n. (Enter your answer as an integer.) payments n = Find the amount of the final payment. (Round your answer to the nearest cent.)

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Answer:

To find the number of payments, n, and the amount of the final payment, we can work through the problem step-by-step.

First, let's determine the interest per period. Since the effective interest rate is 9.5%, we can divide it by 100 to express it as a decimal: 9.5% = 0.095. Therefore, the interest per period is 0.095.

Next, let's calculate the initial interest due on the loan. Since the loan amount is $13,500 and the interest per period is 0.095, the initial interest due can be found by multiplying the loan amount by the interest rate: $13,500 * 0.095 = $1,282.50.

Now, we know that each payment is equal to twice the interest due. Therefore, each payment will be 2 * $1,282.50 = $2,565.

To determine the number of payments, n, we divide the loan amount by the payment amount: $13,500 / $2,565 = 5.27. Since we're interested in the number of whole payments, we round up to the next whole number to account for the final payment. Therefore, the number of payments, n, is 6.

Finally, we need to determine the amount of the final payment, which should be at most $1,800. To find this amount, we subtract the total amount of the previous 5 payments ($2,565 * 5) from the outstanding debt (loan amount - sum of previous payments). That gives us $13,500 - ($2,565 * 5) = $13,500 - $12,825 = $675. Since this amount should be at most $1,800, the final payment is $675.

In summary:

Number of payments, n = 6

Amount of the final payment = $675

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