To calculate the future value of an annuity due using the simple interest formula, we'll use the following information and steps. The simple interest formula for an annuity due is:

Formula for Future Value (FV) of an Annuity Due:

$FV = P \times \left( \frac{(1 + r \cdot t)}{r} \right)$ Where:

• $P$ = annual payment = 14,000
• $r$ = annual interest rate = 5% = 0.05
• $t$ = time in years = 3 years

Step 1: Future Value of Annuity

We apply the formula for annuity due:

$FV = 14,000 \times \left( \frac{(1 + 0.05 \cdot 3)}{0.05} \right)$ This gives:

$FV = 14,000 \times \left( \frac{(1 + 0.15)}{0.05} \right) = 14,000 \times \left( \frac{1.15}{0.05} \right) = 14,000 \times 23$

$FV = 322,000$

So, the future value of the annuity due is $322,000.

Step 2: Amount Invested (Total Payments Made)

The amount invested is the total of all the payments made over the 3 years:

$\text{Amount Invested} = P \times t = 14,000 \times 3 = 42,000$

So, the total amount invested is $42,000.

Step 3: Interest Earned

The interest earned is the difference between the future value and the amount invested:

$\text{Interest Earned} = FV - \text{Amount Invested} = 322,000 - 42,000 = 280,000$

So, the interest earned is $280,000.

Final Answers:

1. Future Value of the Annuity: $322,000
2. Amount Invested: $42,000
3. Interest Earned: $280,000

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Want more details or have any questions about these calculations?

Here are some follow-up questions:

1. How would the future value change if the interest rate was 6% instead of 5%?
2. What is the difference between simple interest and compound interest in this scenario?
3. How would you calculate the future value of an ordinary annuity (not annuity due)?
4. What happens to the future value if the number of years increases?
5. Can you calculate the monthly payment for the same situation using the simple interest formula?

Tip: To use Excel for this, you can use the formula =14000*(1+(0.05*3))/0.05 to find the future value and =14000*3 for the total invested.