Question 1
Points: 1
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 use the following formula:

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

Where:
- $P$ is the payment amount per period ($500),
- $r$ is the interest rate per period (monthly rate = annual rate / 12),
- $n$ is the total number of payments (number of periods).

Given:
- $P = 500$ (monthly payments),
- Annual interest rate = 6%, so the monthly rate $r = \frac{6\%}{12} = 0.005$,
- Time period = 5 years, so the total number of payments $n = 5 \times 12 = 60$.

Now, substitute these values into the formula:

\[
FV_{\text{annuity due}} = 500 \times \left(\frac{(1 + 0.005)^{60} - 1}{0.005}\right) \times (1 + 0.005)
\]

First, calculate intermediate values:

\[
(1 + 0.005)^{60} = 1.34885
\]
\[
\frac{1.34885 - 1}{0.005} = 69.769
\]

Now multiply by the monthly payment and the adjustment for an annuity due:

\[
FV_{\text{annuity due}} = 500 \times 69.769 \times 1.005 = 35,524.40
\]

Thus, the future value of the annuity due is approximately **$35,524.40**.

The correct answer is:

**About $35,524.40**

Would you like more details or have any questions?  
Here are 5 related questions for further practice:
1. How does the future value of an ordinary annuity differ from an annuity due?
2. What is the effect of increasing the interest rate on the future value of an annuity due?
3. How would the future value change if the payments were made quarterly instead of monthly?
4. How can the formula for future value of an annuity due be adapted for different compounding periods?
5. What is the present value of this annuity due, given the same conditions?

**Tip:** In an **annuity due**, payments are made at the beginning of each period, whereas in an **ordinary annuity**, they are made at the end.

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

Learn how to calculate the future value of an annuity due with monthly payments of $500 for 5 years at an annual interest rate of 6%, compounded monthly. This problem demonstrates key concepts in finance, including annuities and compound interest, and is ideal for students in Grades 10-12.

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