To determine the interest earned on a deposit over a period of time with simple interest, you can use the simple interest formula:
[tex]\[ I = P \times r \times t \][/tex]
where:
- [tex]\( P \)[/tex] is the principal amount (the initial amount of money deposited),
- [tex]\( r \)[/tex] is the annual interest rate (expressed as a decimal),
- [tex]\( t \)[/tex] is the time the money is deposited for, in years,
- [tex]\( I \)[/tex] is the interest earned.
Given the values:
- [tex]\( P = 2000 \)[/tex] (the principal amount),
- [tex]\( r = 0.04 \)[/tex] (the annual interest rate as a decimal),
- [tex]\( t = 5 \)[/tex] (the number of years),
we can substitute these values into the formula to find the interest earned.
[tex]\[
I = 2000 \times 0.04 \times 5
\][/tex]
First, multiply the principal by the interest rate:
[tex]\[
2000 \times 0.04 = 80
\][/tex]
Next, multiply this result by the number of years:
[tex]\[
80 \times 5 = 400
\][/tex]
Thus, the interest earned over 5 years is $400.
