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).