Questions: Alonzo invested in a savings bond for 5 years and was paid simple interest at an annual rate of 2%. The total interest he earned was 75. How much did he invest?

Solution Steps

To find out how much Alonzo invested, we can use the formula for simple interest:

\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \]

We know the interest earned, the rate, and the time. We need to solve for the principal (the amount invested). Rearrange the formula to solve for the principal:

\[ \text{Principal} = \frac{\text{Interest}}{\text{Rate} \times \text{Time}} \]

We are given the following values:

• Total interest earned: \( I = 75 \)
• Annual interest rate: \( r = 0.02 \)
• Time period: \( t = 5 \) years

The formula for simple interest is:

\[ I = P \times r \times t \]

where \( P \) is the principal amount (the initial investment). We need to solve for \( P \).

Rearrange the formula to solve for \( P \):

\[ P = \frac{I}{r \times t} \]

Substitute the known values into the formula:

\[ P = \frac{75}{0.02 \times 5} \]

Calculate the principal:

\[ P = \frac{75}{0.1} = 750 \]

Final Answer