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Joseph invests money in an account paying a simple interest of
9% 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?

1.009 m

0.09 m

1.09 m

9m

Joseph invests money in an account paying a simple interest of $9 \%$ 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? $\newline$ $1.009 m$ $\newline$ $0.09 m$ $\newline$ $1.09 m$ $\newline$ $9 m$

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Compound interest

Full solution

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

9 \%

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

1.009 m

\newline

0.09 m

\newline

1.09 m

\newline

9 m

Understand Simple Interest Formula: First, we need to understand the formula for simple interest. The formula is: $\newline$ Interest ( $I$ ) = Principal ( $P$ ) * Rate ( $R$ ) * Time ( $T$ ) $\newline$ Since we are looking for the total balance after a year, we will add the interest to the principal amount. The expression for the total balance ( $B$ ) after one year will be: $\newline$ $B = P + I$
Substitute Given Values: Now, let's substitute the given values into the formula. Joseph invests an amount of money represented by $m$ , the rate is $9\%$ per year, and the time is $1$ year. $\newline$ Using the formula for Interest: $\newline$ $I = m \times 9\% \times 1$ $\newline$ Convert the percentage to a decimal by dividing by $100$ : $\newline$ $I = m \times 0.09 \times 1$
Calculate Interest: Now, calculate the interest: $\newline$ $I = m \times 0.09$
Find Total Balance: Next, we add the interest to the principal to find the total balance after one year: $\newline$ $B = m + I$ $\newline$ $B = m + (m \times 0.09)$
Simplify Expression: Combine like terms to simplify the expression: $\newline$ $B = m \times (1 + 0.09)$ $\newline$ $B = m \times 1.09$

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