last year, jim opened an investment account with $5500. at the end of the year, the amount in the account…

last year, jim opened an investment account with $5500. at the end of the year, the amount in the account had increased by 24.4%. how much is this increase? how much money was in his account at the end of last year? increase in amount: $ year - end amount: $
Answer
Explanation:
Step1: Identify the formula for percentage - increase
Let the initial amount be $x$. The percentage - increase formula is $\text{Percentage increase}=\frac{\text{Final amount}-\text{Initial amount}}{\text{Initial amount}}\times100%$. We know the final amount $A = 5500$, the percentage increase $p = 24.4%=0.244$, and we want to find $x$. Rearranging the formula gives $p=\frac{A - x}{x}$, which can be rewritten as $px=A - x$, then $px+x = A$, and $x=\frac{A}{1 + p}$.
Step2: Calculate the initial amount
Substitute $A = 5500$ and $p = 0.244$ into the formula $x=\frac{A}{1 + p}$. So $x=\frac{5500}{1 + 0.244}=\frac{5500}{1.244}\approx4421.22$.
Step3: Calculate the increase amount
The increase amount is the final amount minus the initial amount. Increase amount $=A - x=5500-4421.22 = 1078.78$.
Answer:
Increase in amount: $$1078.78$ Year - end amount: $$5500$