Questions: Issa notes that her savings account earned 18.37 in e months. If the interest for her account is 3.5%, what her principal? The principal was (Round to the nearest cent.)

Issa notes that her savings account earned 18.37 in e months. If the interest for her account is 3.5%, what her principal? The principal was (Round to the nearest cent.)
Transcript text: issa notes that her savings account eamed $\$ 18.37$ in e months. If the interest for her account is $3.5 \%$, what her principal? The principal was \$ $\square$ ] (Round to the nearest cent.)
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Solution

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Solution Steps

Step 1: Understand the Problem

We are given that Issa's savings account earned $18.37 in interest over a period of \( e \) months. The annual interest rate is \( 3.5\% \). We need to find the principal amount, which is the initial amount of money deposited in the account.

Step 2: Convert the Interest Rate

The interest rate given is an annual rate. Since the interest earned is for \( e \) months, we need to convert the annual interest rate to a monthly rate. The monthly interest rate is:

\[ \text{Monthly Interest Rate} = \frac{3.5\%}{12} = \frac{0.035}{12} \]

Step 3: Use the Simple Interest Formula

The formula for simple interest is:

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

where:

  • \( I \) is the interest earned ($18.37),
  • \( P \) is the principal (unknown),
  • \( r \) is the monthly interest rate,
  • \( t \) is the time in months (\( e \)).

Rearranging the formula to solve for \( P \):

\[ P = \frac{I}{r \times t} \]

Substitute the known values:

\[ P = \frac{18.37}{\left(\frac{0.035}{12}\right) \times e} \]

Step 4: Calculate the Principal

Since we do not have the value of \( e \), we cannot calculate a numerical answer. However, the expression for the principal is:

\[ P = \frac{18.37 \times 12}{0.035 \times e} \]

Final Answer

The principal is given by the expression:

\[ \boxed{P = \frac{18.37 \times 12}{0.035 \times e}} \]

This expression will yield the principal amount when the value of \( e \) is known.

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