Calculate the future value of an annuity due with monthly payments of $500 for 5 years, earning an annual interest rate of 6% compounded monthly. Which of the following is the correct future value?

About $34,885.02

About $33,744.50

About $35,524.40

About $32,744.50

To calculate the **future value (FV) of an annuity due**, we can use the formula:

\[
FV_{\text{due}} = P \times \left[ \frac{(1 + r)^n - 1}{r} \right] \times (1 + r)
\]

Where:
- $P$ = Payment per period = 500  
- $r$ = Monthly interest rate = $ \frac{6\%}{12} = 0.005 $  
- $n$ = Total number of payments = 5 years × 12 = 60  
- $FV_{\text{due}}$ = Future value of the annuity due  

---

### Step-by-Step Calculation:

1. **Calculate (1 + r):**
   \[
   1 + r = 1 + 0.005 = 1.005
   \]

2. **Calculate (1.005)^n:**
   \[
   1.005^{60} \approx 1.34885
   \]

3. **Subtract 1 from the above value:**
   \[
   1.34885 - 1 = 0.34885
   \]

4. **Divide by the monthly interest rate (r):**
   \[
   \frac{0.34885}{0.005} = 69.77
   \]

5. **Multiply by the payment $P$:**
   \[
   500 \times 69.77 = 34,885.02
   \]

6. **Since it is an annuity due, multiply by (1 + r):**
   \[
   34,885.02 \times 1.005 = 35,524.40
   \]

---

### Final Answer:
The **correct future value** of the annuity due is:

\[
\boxed{35,524.40}
\]

---

Would you like further explanation or help with related questions?  
Here are 5 questions to expand on this topic:

1. How does an annuity due differ from an ordinary annuity in terms of future value?  
2. What would the future value be if payments were made annually instead of monthly?  
3. How does the compounding frequency affect the future value?  
4. What is the present value of an annuity due with the same parameters?  
5. How does the interest rate change affect the future value of an annuity?  

**Tip:** Annuities due accumulate more interest than ordinary annuities because payments are made at the beginning of each period, allowing for more compounding.

Calculate the future value of an annuity due with monthly payments of $500 for 5 years, earning an annual interest rate of 6% compounded monthly. Which of the following is the correct future value? About $34,885.02, About $33,744.50, About $35,524.40, About $32,744.50

Calculate the future value of an annuity due with monthly payments of $500 over 5 years at a 6% annual interest rate, compounded monthly. This solution covers the formula for an annuity due and explains key concepts of compound interest and the time value of money. Suitable for students in Grades 10-12 and college.

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