David invests money in an account paying a simple interest of $5.8 \%$ 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? $\newline$ $m+0.058$ $\newline$ $1.0058 m$ $\newline$ $1.058 m$ $\newline$ $5.8 m$

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Grade 8

Compound interest

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

5.8 \%

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

m+0.058

\newline

1.0058 m

\newline

1.058 m

\newline

5.8 m

Understand Simple Interest Formula: First, we need to understand the formula for simple interest. The formula for the total amount after interest is: $\newline$ Total Amount = Principal Amount + (Principal Amount $\times$ Interest Rate $\times$ Time) $\newline$ Since the time is $1$ year, the formula simplifies to: $\newline$ Total Amount = Principal Amount + (Principal Amount $\times$ Interest Rate) $\newline$ Let's denote the Principal Amount by $m$ and the Interest Rate by $5.8\%$ or $0.058$ as a decimal.
Apply Formula to David's Investment: Now, we will apply the simple interest formula to David's investment. $\newline$ Total Amount = $m + (m \times 0.058)$
Simplify Expression by Distributing: Simplify the expression by distributing $m$ . $\newline$ Total Amount = $m + 0.058m$
Combine Like Terms: Combine like terms to get the final expression. $\newline$ Total Amount = $1m + 0.058m$ $\newline$ Total Amount = $1.058m$ $\newline$ This is the expression that represents David's balance after a year with simple interest of $5.8\%$ .