Questions: Money is borrowed at 9% simple interest. After one year, 1140.14 pays off the loan. How much was originally borrowed? The amount of the original loan was

Solution Steps

To find the original amount borrowed, we can use the formula for simple interest:

\[ A = P(1 + rt) \]

where \( A \) is the total amount paid after interest, \( P \) is the principal amount (original amount borrowed), \( r \) is the rate of interest per year, and \( t \) is the time in years. We need to solve for \( P \).

1. Rearrange the formula to solve for \( P \):

\[ P = \frac{A}{1 + rt} \]

2. Substitute the given values into the formula: \( A = 1140.14 \), \( r = 0.09 \), and \( t = 1 \).

We are given the following values:

• Total amount paid after interest, \( A = 1140.14 \)
• Interest rate, \( r = 9\% = 0.09 \)
• Time period, \( t = 1 \) year

The formula for the total amount paid after interest is:

\[ A = P(1 + rt) \]

where \( P \) is the principal amount (original amount borrowed).

Rearrange the formula to solve for the principal amount \( P \):

\[ P = \frac{A}{1 + rt} \]

Substitute the given values into the rearranged formula:

\[ P = \frac{1140.14}{1 + 0.09 \times 1} \]

Calculate the value of \( P \):

\[ P = \frac{1140.14}{1.09} \approx 1046.0 \]

Final Answer