Andres invests money in an account paying a simple interest of $6.8 \%$ per year. If $m$ represents the amount of money he invests, which expression represents his balance after a year, assuming he makes no additional withdrawals or deposits? $\newline$ $1+0.068$ $\newline$ $1.0068 m$ $\newline$ $1.068 m$ $\newline$ $1+0.068 m$

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Grade 7

Compound interest

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

6.8 \%

per year. If

m

represents the amount of money he invests, which expression represents his balance after a year, assuming he makes no additional withdrawals or deposits?

\newline

1+0.068

\newline

1.0068 m

\newline

1.068 m

\newline

1+0.068 m

Understand simple interest: Understand the concept of simple interest. Simple interest is calculated by multiplying the principal amount (the initial amount of money) by the interest rate and by the time the money is invested. $\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}$ Since the time is $1$ year, the formula simplifies to: $\text{Interest} = \text{Principal} \times \text{Rate}$
Convert interest rate to decimal: Convert the interest rate from a percentage to a decimal. The interest rate given is $6.8\%$ , which as a decimal is $0.068$ .
Apply simple interest formula: Apply the simple interest formula to find the interest earned after one year. $\newline$ Interest = $m \times 0.068$
Calculate total balance: Calculate the total balance after one year. $\newline$ The total balance is the sum of the initial investment (principal) and the interest earned. $\newline$ Balance after one year = Principal + Interest $\newline$ Balance after one year = $m + (m \times 0.068)$
Factor out common factor: Factor out the common factor $m$ from the expression. $\newline$ Balance after one year = $m(1 + 0.068)$
Simplify expression: Simplify the expression. $\newline$ Balance after one year = $m (1.068)$ $\newline$ This is the expression that represents Andres's balance after a year with simple interest of $6.8\%$ .