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? 1.0052 m 1.052 m (1+0.052)m 1m+0.052 m

Question

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?  1.0052 m  1.052 m  (1+0.052)m  1m+0.052 m

Bytelearn · Accepted Answer

Understand Simple Interest Formula: We need to understand how simple interest works. The formula for simple interest is: Interest = Principal × Rate × Time 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. Balance after a year = Principal + (Principal × Rate × Time) Balance after a year = m + (m × 0.052 × 1) Balance after a year = m + 0.052m Balance after a year = (1 + 0.052)mCalculate Balance After a Year: Now let's check each expression to see which one does NOT represent the correct balance after a year.  1. 1.0052m This expression seems to represent a 0.52% increase, not a 5.2% increase.Check Incorrect Expressions: 2. 1.052m This expression seems to correctly represent a 5.2% increase.Identify Incorrect Expression: 3. (1+0.052)m This expression is the same as the one we derived, which correctly represents a 5.2% increase.4. 1m + 0.052m 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.

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