To find the future value of an annuity due with simple interest, we will use the simple interest formula and adjust it for an annuity due.

Step 1: Understanding the Formula

The future value $FV$ of an annuity due can be calculated by this formula: $FV = P \times \left(1 + r \times t \right) \times \left(1 + r\right)$ Where:

• $P$ = Payment amount per period (in this case, $11,000)
• $r$ = Interest rate per period (3% = 0.03)
• $t$ = Number of periods (3 years)
• The factor $(1 + r)$ is included for an annuity due because payments are made at the start of each period.

Step 2: Calculate the Future Value

Substitute the given values into the formula: $FV = 11,000 \times \left(1 + 0.03 \times 3 \right) \times \left(1 + 0.03\right)$ $FV = 11,000 \times (1 + 0.09) \times (1.03)$ $FV = 11,000 \times 1.09 \times 1.03$ $FV = 11,000 \times 1.1227 = 12,399.70$

Step 3: How much was invested?

The total amount invested is simply the annual payment multiplied by the number of periods: $\text{Total Invested} = 11,000 \times 3 = 33,000$

Step 4: How much interest was earned?

Interest earned is the difference between the future value and the total invested amount: $\text{Interest Earned} = FV - \text{Total Invested}$ $\text{Interest Earned} = 12,399.70 - 33,000 = -20,600.30$

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