Kadeesha 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 she multiply her current balance by to find her total balance in a year in one step? $\newline$ Answer:

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Grade 7

Compound interest

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Q. Kadeesha 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 she multiply her current balance by to find her total balance in a year in one step?

\newline

Answer:

Understand Simple Interest: Understand the concept of simple interest. Simple interest is calculated by multiplying the principal amount (the initial sum of money) by the interest rate and by the number of time periods. The formula for simple interest is $I = P \times r \times t$ , where $I$ is the interest earned, $P$ is the principal amount, $r$ is the interest rate per time period, and $t$ is the number of time periods. Since we want to find the total balance after one year, we need to calculate the principal plus the interest earned.
Convert Interest Rate to Decimal: Convert the interest rate to a decimal. $\newline$ The interest rate given is $2\%$ per year. To use this in calculations, we need to convert it to a decimal by dividing by $100$ . $\newline$ $2\% = \frac{2}{100} = 0.02$
Calculate Multiplier for Total Balance: Calculate the multiplier for the total balance after one year. $\newline$ To find the total balance, we add the interest earned to the principal amount. Since the interest is $2\%$ of the principal, the total balance will be $100\%$ of the principal plus $2\%$ of the principal. $\newline$ Total balance $= \text{Principal} + (\text{Principal} \times \text{Interest Rate})$ $\newline$ Total balance $= \text{Principal} \times (1 + \text{Interest Rate})$ $\newline$ Total balance $= \text{Principal} \times (1 + 0.02)$ $\newline$ Total balance $= \text{Principal} \times 1.02$ $\newline$ Kadeesha should multiply her current balance by $1.02$ to find her total balance in a year.