Evan invests money in an account paying a simple interest of $2 \%$ per year. If no money will be added or removed from the investment, what should he multiply his current balance by to find his total balance in a year in one step? $\newline$ Answer:

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Q. Evan invests money in an account paying a simple interest of

2 \%

per year. If no money will be added or removed from the investment, what should he multiply his current balance by to find his total balance in a year in one step?

\newline

Answer:

Calculate Simple Interest: To find the total balance after one year with simple interest, we need to calculate the interest earned and add it to the original balance. The formula for simple interest is $I = P \times r \times t$ , where $I$ is the interest, $P$ is the principal amount (initial investment), $r$ is the annual interest rate (as a decimal), and $t$ is the time in years.
Convert Annual Rate to Decimal: Since Evan's annual interest rate is $2\%$ , we convert this percentage to a decimal by dividing by $100$ . So, $r = \frac{2}{100} = 0.02$ .
Determine Time Period: The time $t$ is $1$ year, as we are looking for the total balance after one year.
Calculate Interest Earned: Now, we can calculate the interest earned in one year. Using the formula $I = P \times r \times t$ , we get $I = P \times 0.02 \times 1$ .
Calculate Interest Amount: The interest earned in one year is $2\%$ of the principal amount, which means Evan should multiply his current balance by $0.02$ to find the interest earned.
Find Total Balance: To find the total balance, Evan needs to add the original principal amount to the interest earned. This means he should multiply his current balance by $1$ (to account for the original balance) and then add the interest earned ( $2\%$ of the balance). So, the total balance can be found by multiplying the current balance by $1.02$ ( $1 + 0.02$ ).