Mia invests $10,000 in an index fund. After 1 year, the fund's share price has increased by 4%. How much did Mia gain?
The problem provides an initial investment amount, which we denote as the principal \(P = \$10,000\). We are given that the investment grows at an annual rate of \(r = 4\%\). We need to determine the monetary gain Mia achieved after one year. The gain is calculated as the product of the principal and the rate of growth.
To find the gain, we use the formula:
\[ \text{Gain} = P \times r \]
where \(P\) is the initial investment and \(r\) is the annual growth rate expressed as a decimal. Given \(P = \$10,000\) and \(r = 4\% = 0.04\), we substitute these values into the formula:
\[ \text{Gain} = \$10,000 \times 0.04 \]
Performing the multiplication:
\[ \text{Gain} = \$400 \]
Thus, the monetary gain Mia made on her investment is \(\$400\).
Understanding investment growth is essential for personal finance and planning for the future. For example, if you deposit \(\$5,000\) into a high-yield savings account that offers a \(2.5\%\) annual interest rate, you can calculate your earnings after one year by finding \(0.025 \times \$5,000 = \$125\). This simple math helps you evaluate the effectiveness of different savings vehicles and make informed decisions about where to keep your money.