To determine the number of months it would take Megan Dunstall to earn \[tex]$618.75 in simple interest on \$[/tex]15,000 at a 5.5% interest rate, we need to follow these steps:
1. Understand the Simple Interest Formula:
The formula for simple interest is:
[tex]\[
I = P \times r \times t
\][/tex]
where [tex]\(I\)[/tex] is the interest, [tex]\(P\)[/tex] is the principal amount, [tex]\(r\)[/tex] is the annual interest rate, and [tex]\(t\)[/tex] is the time in years.
2. Identify the Known Values:
- [tex]\(P = \$15,000\)[/tex] (principal)
- [tex]\(I = \$618.75\)[/tex] (interest earned)
- [tex]\(r = 5.5\% \text{ per year} = 0.055\)[/tex] (converted to a decimal)
3. Rearrange the Formula to Find Time [tex]\(t\)[/tex]:
We need to solve for [tex]\(t\)[/tex]:
[tex]\[
t = \frac{I}{P \times r}
\][/tex]
4. Substitute the Values into the Formula:
Substitute the known values into the formula:
[tex]\[
t = \frac{618.75}{15,000 \times 0.055}
\][/tex]
5. Calculate the Time in Years:
[tex]\[
t = \frac{618.75}{825} = 0.75 \text{ years}
\][/tex]
6. Convert Time from Years to Months:
Since there are 12 months in a year, convert the time from years to months:
[tex]\[
t_{\text{months}} = 0.75 \times 12 = 9 \text{ months}
\][/tex]
Therefore, it would take Megan Dunstall 9 months to earn \[tex]$618.75 in simple interest on her \$[/tex]15,000 savings account at a 5.5% interest rate.
