Adam invests money in an account paying a simple interest of $6 \%$ 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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Grade 8

Probability of independent and dependent events

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

6 \%

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 Interest Formula: 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: $\newline$ Interest $= Principal \times Rate \times Time$ $\newline$ Where $Principal$ is the initial amount of money, $Rate$ is the interest rate per period, and $Time$ is the number of periods.
Adam's Interest Rate: Adam's interest rate is $6\%$ per year, which can be written as $0.06$ in decimal form. Since we are looking for the total balance after one year, Time is $1$ .
Calculate Interest Earned: Using the formula for simple interest, the interest Adam would earn in one year on a principal amount (which we'll call $P$ ) is: $\newline$ $\text{Interest} = P \times 0.06 \times 1$ $\newline$ $\text{Interest} = 0.06P$
Find Total Balance: To find the total balance, we add the interest earned to the original principal: $\newline$ Total Balance = Principal + Interest $\newline$ Total Balance = $P + 0.06P$ $\newline$ Total Balance = $1P + 0.06P$ $\newline$ Total Balance = $(1 + 0.06)P$ $\newline$ Total Balance = $1.06P$
Multiply by $1.06$ : Therefore, Adam should multiply his current balance by $1.06$ to find his total balance after one year.