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Assume that you take out a $2000 loan for 49 months at 4.5% APR. How much total interest will you have paid at the end of the 49 months? (Round your answer to the nearest cent.)

User Datosula
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To calculate the total interest paid on a loan, we need to use the formula:

Total interest = Total amount paid - Principal

where Total amount paid = Monthly payment x Number of months and Principal is the amount of the loan.

First, let's calculate the monthly payment using the formula for a fixed-payment loan:

Monthly payment = [Principal x Rate x (1 + Rate)^N] / [(1 + Rate)^N - 1]

where Rate is the monthly interest rate (4.5% APR divided by 12), and N is the total number of payments (49 months).

Rate = 4.5% / 12 = 0.375%

N = 49

Monthly payment = [2000 x 0.00375 x (1 + 0.00375)^49] / [(1 + 0.00375)^49 - 1] = $45.99 (rounded to the nearest cent)

Now, we can calculate the total amount paid over the life of the loan:

Total amount paid = Monthly payment x Number of months = $45.99 x 49 = $2,253.51

Finally, we can calculate the total interest paid:

Total interest = Total amount paid - Principal = $2,253.51 - $2,000 = $253.51

Therefore, the total interest paid at the end of the 49 months is $253.51 (rounded to the nearest cent).

User Andrii Tsok
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