Question

Alonso invests money in an account paying a simple interest of 2, percent2% per year. If mm represents the amount of money he invests, which expression represents his balance after a year, assuming he makes no additional withdrawals or deposits?

Answer 1

To find Alonso's balance after a year with simple interest, we can use the formula for simple interest:

\[
\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}
\]

where:
- Principal is the initial amount invested (denoted as \( mm \)),
- Rate is the annual interest rate (2% per year, which can be expressed as a decimal, so \( 0.02 \)),
- Time is the number of years the money is invested (in this case, 1 year).

Now, plugging in the values:

\[
\text{Interest} = mm \times 0.02 \times 1 = 0.02 \cdot mm
\]

To find the total balance after one year, we add the interest earned to the principal:

\[
\text{Total Balance} = \text{Principal} + \text{Interest} = mm + 0.02 \cdot mm
\]

This can be factored as:

\[
\text{Total Balance} = mm(1 + 0.02) = mm(1.02)
\]

Thus, the expression that represents Alonso's balance after a year is:

\[
mm(1.02)
\]