last year, laura opened an investment account with $5200. at the end of the year, the amount in the account…

last year, laura opened an investment account with $5200. at the end of the year, the amount in the account had decreased by 7.5%. how much money was in her account at the end of last year? decrease in amount: $____ year - end amount: $____

last year, laura opened an investment account with $5200. at the end of the year, the amount in the account had decreased by 7.5%. how much money was in her account at the end of last year? decrease in amount: $____ year - end amount: $____

Answer

Explanation:

Step1: Identify the formula for percentage - decrease.

Let the initial amount be $x$. The formula for the final amount $A$ after a percentage - decrease of $p%$ is $A=(1 - \frac{p}{100})x$. We know $A = 5200$ and $p = 7.5$. We want to find the decrease amount $D$ and the initial amount $x$. First, rewrite the formula as $x=\frac{A}{1 - \frac{p}{100}}$.

Step2: Calculate the initial amount $x$.

Substitute $A = 5200$ and $p = 7.5$ into the formula $x=\frac{A}{1-\frac{p}{100}}$. Since $1-\frac{7.5}{100}=1 - 0.075=0.925$, then $x=\frac{5200}{0.925}=\frac{5200}{\frac{925}{1000}}=\frac{5200\times1000}{925}=\frac{5200000}{925}=\frac{208000}{37}\approx5621.62$.

Step3: Calculate the decrease amount $D$.

The decrease amount $D=x - A$. Substitute $x=\frac{208000}{37}$ and $A = 5200$. $D=\frac{208000}{37}-5200=\frac{208000 - 5200\times37}{37}=\frac{208000-192400}{37}=\frac{15600}{37}\approx421.62$.

Answer:

Decrease in amount: $$421.62$ Year - end amount: $$5200$