Eric took out a loan for 292 days and was charged simple interest at an annual rate of \( 2.5 \% \). The total interest he paid on the loan was \( \$ 146 \). How much money did Eric borrow? Assume that there are 365 days in a year, and do not round any intermediate computations. If necessary, refer to the list of financial formulas.

To find out how much money Eric borrowed, we can use the formula for simple interest: \[ I = P \times r \times t \] where \( I \) is the interest paid, \( P \) is the principal amount (the amount borrowed), \( r \) is the annual interest rate (as a decimal), and \( t \) is the time in years. Given that: - \( I = 146 \) - \( r = 2.5\% = 0.025 \) - \( t = \frac{292}{365} \) We can rearrange the formula to solve for \( P \): \[ P = \frac{I}{r \times t} \] First, calculate \( t \): \[ t = \frac{292}{365} \approx 0.7992 \] Now substitute the values into the rearranged formula: \[ P = \frac{146}{0.025 \times 0.7992} \] Now calculate \( r \times t \): \[ 0.025 \times 0.7992 \approx 0.01998 \] Finally, find \( P \): \[ P = \frac{146}{0.01998} \approx 7306.14 \] So, Eric borrowed approximately \( \$ 7306.14 \). Now, let's add a fun fact and practical application! Did you know that simple interest is often used in personal loans, auto loans, and some types of mortgages? It offers predictability since the interest doesn't compound, making it easier for borrowers to budget their repayments without unexpected increases. Another tip is always to check the total amount you’ll repay, including interest, before taking a loan. This way, you can plan and avoid surprises, especially with longer loan terms or larger amounts.