melissa notes that her savings account earned $54.78 in nine months. if the interest for her account is…

melissa notes that her savings account earned $54.78 in nine months. if the interest for her account is 6.5%, what was her principal? the principal was $ (round to the nearest cent.)

melissa notes that her savings account earned $54.78 in nine months. if the interest for her account is 6.5%, what was her principal? the principal was $ (round to the nearest cent.)

Answer

Explanation:

Step1: Convert time to years

Nine months is $\frac{9}{12}= 0.75$ years.

Step2: Use simple - interest formula

The simple - interest formula is $I = Prt$, where $I$ is the interest, $P$ is the principal, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. We know $I = 54.78$, $r=0.065$, and $t = 0.75$. We need to solve for $P$. Rearranging the formula gives $P=\frac{I}{rt}$.

Step3: Substitute values and calculate

Substitute $I = 54.78$, $r = 0.065$, and $t=0.75$ into the formula: $P=\frac{54.78}{0.065\times0.75}=\frac{54.78}{0.04875}\approx1123.7$.

Answer:

$1123.70$