Find the payment that should be used for the annuity due whose future value is given assume that the compounding period is the same as the payment period. 2000; quarterly payments for 6 years; interest rate 3.7%

To find the payment for an **annuity due** where the future value is known, we can use the **Future Value of an Annuity Due (FVAD)** formula:

\[
FVAD = P \times \left( \frac{(1 + i)^n - 1}{i} \right) \times (1 + i)
\]

Where:
- $FVAD$ is the future value of the annuity due.
- $P$ is the payment per period (this is what we are solving for).
- $i$ is the interest rate per period.
- $n$ is the total number of payments.

### Given Information:
- Future Value ($FVAD$) = 2000
- Quarterly payments for 6 years: $n = 4 \times 6 = 24$ periods.
- Interest rate = 3.7% per year, quarterly compounding: $i = \frac{3.7\%}{4} = 0.00925$ per period.

Now, let's rearrange the formula to solve for $P$:

\[
P = \frac{FVAD}{\left( \frac{(1 + i)^n - 1}{i} \right) \times (1 + i)}
\]

Let me calculate the payment for this annuity due.The payment that should be made for the annuity due is approximately **$74.12** per quarter.

Would you like further details on the steps or any additional questions? Here are some related questions you might find useful:

1. What is the difference between an annuity due and an ordinary annuity?
2. How would the payment change if the interest rate were different?
3. How is the present value of an annuity calculated?
4. What happens if payments are made monthly instead of quarterly?
5. How does inflation impact the future value of an annuity?

**Tip:** An annuity due involves payments made at the beginning of each period, as opposed to at the end for an ordinary annuity.

Find the payment that should be used for the annuity due whose future value is given. Assume that the compounding period is the same as the payment period. 2000; quarterly payments for 6 years; interest rate 3.7%

Learn how to calculate the payment for an annuity due with a future value of $2000, quarterly payments over 6 years, and a 3.7% annual interest rate. This problem demonstrates the use of the Future Value of an Annuity Due (FVAD) formula and is suitable for college-level finance or business students.

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