Ella invests money in an account paying a simple interest of $5.2 \%$ per year. If $m$ represents the amount of money she invests, which expression does NOT represent her balance after a year, assuming she makes no additional withdrawals or deposits? $\newline$ $1.0052 m$ $\newline$ $1.052 m$ $\newline$ $(1+0.052) m$ $\newline$ $1 m+0.052 m$

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Math Problems

Grade 7

Compound interest

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

5.2 \%

per year. If

m

represents the amount of money she invests, which expression does NOT represent her balance after a year, assuming she makes no additional withdrawals or deposits?

\newline

1.0052 m

\newline

1.052 m

\newline

(1+0.052) m

\newline

1 m+0.052 m

Understand Simple Interest Formula: We need to understand how simple interest works. The formula for simple interest is: $\newline$ Interest = Principal $\times$ Rate $\times$ Time $\newline$ Since we are looking for the balance after a year, we need to add the interest to the principal amount. The rate given is $5.2\%$ , which as a decimal is $0.052$ . The time is $1$ year. $\newline$ Balance after a year = Principal + (Principal $\times$ Rate $\times$ Time) $\newline$ Balance after a year = $m + (m \times 0.052 \times 1)$ $\newline$ Balance after a year = $m + 0.052m$ $\newline$ Balance after a year = $(1 + 0.052)m$
Calculate Balance After a Year: Now let's check each expression to see which one does NOT represent the correct balance after a year. $\newline$ $1$ . $1.0052m$ $\newline$ This expression seems to represent a $0.52\%$ increase, not a $5.2\%$ increase.
Check Incorrect Expressions: $2$ . $1.052m$ $\newline$ This expression seems to correctly represent a $5.2\%$ increase.
Identify Incorrect Expression: $3$ . $(1+0.052)m$ $\newline$ This expression is the same as the one we derived, which correctly represents a $5.2\%$ increase.
Identify Incorrect Expression: $3$ . $(1+0.052)m$ $\newline$ This expression is the same as the one we derived, which correctly represents a $5.2\%$ increase. $4$ . $1m + 0.052m$ $\newline$ This expression is also the same as the one we derived, just written differently. It correctly represents a $5.2\%$ increase.
Identify Incorrect Expression: $3$ . $(1+0.052)m$ $\newline$ This expression is the same as the one we derived, which correctly represents a $5$ . $2$ % increase. $4$ . $1m + 0.052m$ $\newline$ This expression is also the same as the one we derived, just written differently. It correctly represents a $5$ . $2$ % increase.The expression that does NOT represent the correct balance after a year is the first one, $1.0052m$ , because it represents a $0$ . $52$ % increase instead of the correct $5$ . $2$ % increase.