Questions: Reibursed in a savings bond for 4 years and was paid annual interest at an annual rate of 2%. The total interest that he earned was 561. How much did he invest?

Solution Steps

To find out how much Reibursed invested, we can use the formula for compound interest. However, since the interest is paid annually and the rate is relatively low, we can approximate using the simple interest formula for a quick estimation. The formula for simple interest is:

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

where:

• \( I \) is the interest earned ($561)
• \( P \) is the principal amount (the initial investment)
• \( r \) is the annual interest rate (2% or 0.02)
• \( t \) is the time in years (4 years)

We need to solve for \( P \).

1. Use the simple interest formula to set up the equation.
2. Rearrange the equation to solve for \( P \).

We start with the simple interest formula:

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

where:

• \( I = 561 \) (total interest earned)
• \( r = 0.02 \) (annual interest rate)
• \( t = 4 \) (time in years)

To find the principal amount \( P \), we rearrange the formula:

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

Substituting the known values into the rearranged formula gives:

\[ P = \frac{561}{0.02 \times 4} \]

Calculating the denominator:

\[ 0.02 \times 4 = 0.08 \]

Now substituting back:

\[ P = \frac{561}{0.08} = 7012.5 \]

Final Answer