
What is the accumulated sum of the following stream of payments?
$17,319 every year at the beginning of the year for 13 years, at 8.96 percent, compounded annually.

Round the answer to two decimal places.

To find the accumulated sum of a stream of payments where payments are made at the beginning of each year, we need to use the formula for the future value of an annuity due. The future value of an annuity due is calculated as follows:

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

Where:
- $ P $ is the annual payment ($17,319),
- $ r $ is the annual interest rate (8.96% or 0.0896),
- $ n $ is the number of payments (13 years).

Let's calculate it step by step.

1. **Calculate the future value factor**:
   \[
   \text{Future Value Factor} = \frac{(1 + r)^n - 1}{r}
   \]
   \[
   \text{Future Value Factor} = \frac{(1 + 0.0896)^{13} - 1}{0.0896}
   \]

2. **Calculate the future value**:
   \[
   FV_{\text{due}} = 17,319 \times \text{Future Value Factor} \times (1 + 0.0896)
   \]

Let's compute this.The accumulated sum of the stream of payments is **$432,008.42** when rounded to two decimal places.

Would you like any further details or have any questions?

Here are five related questions you might find interesting:

1. How would the accumulated sum change if the payments were made at the end of each year?
2. What would be the accumulated sum if the interest rate were 7% instead of 8.96%?
3. How would the future value change if the payments were made monthly instead of annually?
4. What is the present value of the same stream of payments?
5. How would an increase in the number of payment years affect the future value?

**Tip:** When dealing with annuities due (payments at the beginning of each period), remember that the future value is always slightly higher compared to an ordinary annuity (payments at the end of each period) due to the extra compounding period.

What is the accumulated sum of the following stream of payments? $17,319 every year at the beginning of the year for 13 years, at 8.96 percent, compounded annually. Round the answer to two decimal places.

Calculate the future value of an annuity due with annual payments of $17,319 at the beginning of each year for 13 years, compounded annually at 8.96%. Learn the step-by-step process using key financial concepts and formulas. Ideal for college-level finance or mathematics students.

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