To calculate the interest earned on an investment over a certain period of time with a fixed interest rate, we can use the formula for simple interest, which is:
[tex]\[ \text{Simple Interest} = P \times r \times t \][/tex]
where:
- [tex]\( P \)[/tex] is the principal amount (the initial amount of money),
- [tex]\( r \)[/tex] is the annual interest rate (expressed as a decimal), and
- [tex]\( t \)[/tex] is the time the money is invested for, in years.
Given the problem, we have:
- Principal [tex]\( P = \$571 \)[/tex]
- Annual interest rate [tex]\( r = 5\% \)[/tex] (To convert a percentage to a decimal, we divide by 100, so [tex]\( r = \frac{5}{100} = 0.05 \)[/tex])
- Time [tex]\( t = 4 \)[/tex] years
Plugging these values into the formula, we get:
[tex]\[ \text{Simple Interest} = \$571 \times 0.05 \times 4 \][/tex]
Now, perform the multiplication:
[tex]\[ \text{Simple Interest} = \$571 \times 0.2 \][/tex]
[tex]\[ \text{Simple Interest} = \$114.2 \][/tex]
Therefore, a [tex]$571 investment will earn $[/tex]114.2 in interest at a 5% annual rate over four years.
