Questions: Henry took out a loan for 7500 and was charged simple interest at an annual rate of 4.7%. The total interest he paid on the loan was 141. How long was the loan for, in days? 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. days

Solution Steps

The formula for simple interest is given by:

\[ I = P \times r \times t \]

where:

• \( I \) is the interest,
• \( P \) is the principal amount,
• \( r \) is the annual interest rate (in decimal form),
• \( t \) is the time in years.

We know:

• \( I = 141 \) (the total interest paid),
• \( P = 7500 \) (the principal amount),
• \( r = 4.7\% = 0.047 \) (the annual interest rate).

Substituting these values into the formula, we have:

\[ 141 = 7500 \times 0.047 \times t \]

Rearrange the equation to solve for \( t \):

\[ t = \frac{141}{7500 \times 0.047} \]

Calculate \( t \):

\[ t = \frac{141}{352.5} \approx 0.4000 \text{ years} \]

Since there are 365 days in a year, convert the time from years to days:

\[ t_{\text{days}} = 0.4000 \times 365 \approx 146 \text{ days} \]

Final Answer