Full solution

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

1 \%

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 m

\newline

1.01 \mathrm{~m}

\newline

1.001 \mathrm{~m}

\newline

0.01 \mathrm{~m}

Identify variables and formula: Identify the variables and the formula for simple interest. $\newline$ Simple interest is calculated using the formula $I = P \times r \times t$ , where $I$ is the interest earned, $P$ is the principal amount (initial investment), $r$ is the annual interest rate, and $t$ is the time in years. Since we are looking for the balance after a year, we need to add the interest earned to the initial investment.
Convert interest rate to decimal: Convert the annual interest rate from a percentage to a decimal. $\newline$ The interest rate given is $1\%$ , which as a decimal is $0.01$ (since $1\% = \frac{1}{100} = 0.01$ ).
Calculate interest earned: Calculate the interest earned after one year. $\newline$ Using the formula for simple interest, we have $I = m \times 0.01 \times 1$ , where $m$ is the initial investment and we multiply by $1$ because the time period is one year.
Calculate total balance: Calculate the total balance after one year. $\newline$ The total balance is the initial investment plus the interest earned, so the balance after one year is $m + I$ . Substituting the expression for $I$ from Step $3$ , we get $m + (m \times 0.01 \times 1)$ .
Simplify total balance expression: Simplify the expression for the total balance. Simplify the expression $m + (m \times 0.01 \times 1)$ to $m + 0.01m$ , which can be further simplified to $1m + 0.01m$ .
Combine like terms: Combine like terms to get the final expression. $\newline$ Combine $1m$ and $0.01m$ to get $1.01m$ . This is the expression that represents Anthony's balance after a year with simple interest of $1\%$ per year.