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Answer: The loan was taken for 265 days.
We arrive at the answer as follows:
First we find the ratio of interest paid to the total loan amount to determine the interest rate:
Interest paid = $1,307
Loan Amount = $45,000
Since the interest rate calculated above is less than the annual interest rate at 4%, we conclude that the loan taken was for a period of less than one year.
We can determine the period for which the loan was taken as follows:
Let 'x' be the time for which the loan was taken.
We need to solve for x in the proportion below
0.04 : 365 :: 0.029044444:x
Solving we get,