
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?
A.
About $34,885.02
B.
About $33,744.50
C.
About $35,524.40
D.
About $32,744.50

To calculate the future value of an annuity due, we use the formula:

\[
FV = P \times \frac{(1 + r)^n - 1}{r} \times (1 + r)
\]

where:
- $ P $ is the monthly payment,
- $ r $ is the monthly interest rate,
- $ n $ is the total number of payments,
- $ (1 + r) $ accounts for the fact that this is an annuity due, meaning payments are made at the beginning of each period.

### Step-by-Step Solution:
1. **Identify the known values:**
   - $ P = 500 $ (monthly payment)
   - Annual interest rate = 6%, so the monthly interest rate $ r = \frac{6\%}{12} = 0.5\% = 0.005 $
   - Number of years = 5, so the total number of payments $ n = 5 \times 12 = 60 $.

2. **Substitute the values into the formula:**

   \[
   FV = 500 \times \frac{(1 + 0.005)^{60} - 1}{0.005} \times (1 + 0.005)
   \]

3. **Calculate each part:**
   - Calculate $ (1 + 0.005)^{60} \approx 1.34885 $
   - Find $ \frac{1.34885 - 1}{0.005} = 69.77 $
   - Multiply by the monthly payment and adjustment for annuity due: 
     \[
     500 \times 69.77 \times 1.005 \approx 35,524.40
     \]

### Final Answer:
The correct choice is:
**C. About $35,524.40**

Would you like to see further details or have any questions? 

#### Related Questions:
1. How does an ordinary annuity differ from an annuity due?
2. How would the future value change if the payments were made at the end of each period?
3. How would you calculate the present value of this annuity due?
4. What if the interest were compounded quarterly instead of monthly—how would that affect the future value?
5. What would the future value be if the interest rate increased to 8%?

#### Tip:
For annuities due, remember that payments are made at the beginning of each period, which slightly increases the future value due to the additional compounding for each payment.

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? A. About $34,885.02 B. About $33,744.50 C. About $35,524.40 D. About $32,744.50

Learn how to calculate the future value of an annuity due with monthly payments of $500 for 5 years, compounded monthly at an annual interest rate of 6%. Includes a detailed formula and step-by-step solution. Ideal for high school students studying finance or algebra.

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