Interest and TVM Melissa notes that her savings account eamed \( \$ 18.37 \) in three months. It the interest for her account is \( 5.5 \% \), what was her principal?

To find the principal, we can use the formula for simple interest: \( I = P \times r \times t \). Here, \( I \) is the interest earned (\$18.37), \( r \) is the annual interest rate (5.5% or 0.055), and \( t \) is the time in years (3 months or \( \frac{3}{12} = 0.25 \) years). Rearranging the formula to solve for \( P \) gives us: \( P = \frac{I}{r \times t} \). Plugging in the values: \( P = \frac{18.37}{0.055 \times 0.25} = \frac{18.37}{0.01375} \approx 1330.40 \). So, her principal amount was approximately \( \$1330.40 \). When it comes to understanding interest and time value of money (TVM), it's key to grasp how money can grow over time, thanks to interest. For example, if Melissa deposits that principal amount in the bank with consistent contributions, she can watch her savings blossom thanks to the magic of compounding! Understanding these concepts can also help in making smarter investments for the future. A common mistake people make is neglecting the fact that not all interest is created equal. For instance, some accounts offer compound interest, which can give bigger returns over time compared to simple interest. Always check if the interest is compounded annually, semi-annually, quarterly, or monthly, as this will significantly affect your savings potential! So, be sure to read the fine print before you deposit.