Dijon invested $5000 in a fund for 4 years and was paid simple interest. The total interest that she received on the investment was $400. As a percentage, what was the annual interest rate of her investment? If necessary refer to the list of financial formulas
Simple interest is calculated using the formula:
\[ I = P \cdot r \cdot t \]
where:
- \( I \) is the total interest earned,
- \( P \) is the principal amount (the initial amount of money),
- \( r \) is the annual interest rate (in decimal form),
- \( t \) is the time the money is invested for, in years.
We know that Dijon received a total interest (\( I \)) of $400, invested a principal amount (\( P \)) of $5000, and the time (\( t \)) was 4 years. We need to find the annual interest rate (\( r \)).
Let's rearrange the formula to solve for \( r \):
\[ r = \frac{I}{P \cdot t} \]
Now we can plug in the values:
\[ r = \frac{400}{5000 \cdot 4} = \frac{400}{20000} = 0.02 \]
To express \( r \) as a percentage, we multiply by 100:
\[ r \times 100 = 0.02 \times 100 = 2\% \]
Therefore, the annual interest rate of her investment was 2%.