To determine the amount of interest earned and the total amount on a principal of \[tex]$5,000 at an 8% annual interest rate over a period of 20 years, we can use the formula for simple interest:
\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \]
Given:
- Principal (\( P \)) = \$[/tex]5,000
- Rate ([tex]\( R \)[/tex]) = 8% = 0.08
- Time ([tex]\( T \)[/tex]) = 20 years
1. Calculate the amount of interest earned:
Substituting the given values into the formula:
[tex]\[
\text{Interest} = 5000 \times 0.08 \times 20
\][/tex]
Performing the multiplication:
[tex]\[
\text{Interest} = 8000
\][/tex]
Therefore, the amount of interest earned is \[tex]$8,000.
2. Calculate the total amount after interest:
To find the total amount, we add the principal to the interest earned:
\[
\text{Total Amount} = \text{Principal} + \text{Interest}
\]
Substituting the known values:
\[
\text{Total Amount} = 5000 + 8000
\]
Performing the addition:
\[
\text{Total Amount} = 13000
\]
Therefore, the total amount after interest is \$[/tex]13,000.
So, the amount of interest earned on \[tex]$5,000 at an 8% annual interest rate for 20 years is \$[/tex]8,000, and the total amount after 20 years is \$13,000.
