Question

grace invests money in an account paying a simple interest of 6.9% 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?

answer

○ 1m + 0.069m ○ (1 + 0.069)m
○ 1.0069m ○ m + 0.069m

Explanation:

Step1: Recall simple interest formula for balance

The formula for simple interest balance after 1 year is \( \text{Balance} = \text{Principal} + \text{Interest} \). The interest is \( I = Prt \), here \( t = 1 \) year, \( r = 6.9\%= 0.069 \), principal \( P = m \). So interest \( I= m\times0.069\times 1= 0.069m \), balance is \( m + 0.069m \).

Step2: Simplify the balance expression

• \( m + 0.069m=1m + 0.069m \) (since \( m = 1m \))
• Factor out \( m \): \( m(1 + 0.069)=(1 + 0.069)m \)
• Calculate \( 1+ 0.069 = 1.069 \), so balance is \( 1.069m \), not \( 1.0069m \).

Answer:

\( 1.0069m \)