Kevin invested in a savings bond for two years and was paid simple interest at an annual rate of 2%. The total interest that he earned was $80. How much did he invest? If necessary refer to the list of financial formulas.
To calculate the initial investment amount, Kevin made in the savings bond, we can use the simple interest formula:
\[ I = P \times r \times t \]
where:
- \( I \) is the total interest earned ($80),
- \( P \) is the principal amount (the initial investment we are trying to find),
- \( r \) is the annual interest rate (2% or 0.02 as a decimal),
- \( t \) is the time the money is invested in years (2 years).
We rearrange the formula to solve for \( P \):
\[ P = \frac{I}{r \times t} \]
Now, we substitute \( I \), \( r \), and \( t \) with known values:
\[ P = \frac{80}{0.02 \times 2} \]
\[ P = \frac{80}{0.04} \]
\[ P = 2000 \]
Kevin invested $2000 in a savings bond.