Here is your data. Periodic deposit: $9000 at the end of each year. Rate: 3.5% compounded annually. Time: 20 years.  Determine the value of the annuity in dollars using the appropriate formula. Do not round the final answer. Then round to the nearest dollar as needed.

To determine the value of the annuity using the given data, we will use the **future value of an ordinary annuity formula**:

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

Where:
- $FV$ = Future value of the annuity
- $P$ = Periodic deposit (9000 dollars)
- $r$ = Interest rate per period (3.5% = 0.035)
- $t$ = Number of periods (20 years)

Let's plug in the values:

\[
FV = 9000 \times \frac{(1 + 0.035)^{20} - 1}{0.035}
\]

Now, let's calculate this step by step.The future value of the annuity is approximately $ 254,517.136 $ dollars. 

Now, rounding this to the nearest dollar, the future value of the annuity is $ 254,517 $ dollars.

Would you like more details, or do you have any questions?

Here are five related questions for further exploration:
1. What is the difference between an ordinary annuity and an annuity due?
2. How does increasing the interest rate affect the future value of the annuity?
3. What if the interest were compounded monthly instead of annually? How would that change the calculation?
4. How would the future value change if deposits were made at the beginning of each year?
5. How does the time period impact the growth of an annuity?

**Tip:** Always ensure that the interest rate and the compounding period are consistent when using annuity formulas. For example, annual compounding requires an annual interest rate.

Here is your data. Periodic deposit: $9000 at the end of each year. Rate: 3.5% compounded annually. Time: 20 years. Determine the value of the annuity in dollars using the appropriate formula. Do not round the final answer. Then round to the nearest dollar as needed.

Calculate the future value of an annuity with a $9000 annual deposit at 3.5% interest compounded annually over 20 years. Learn step-by-step how to use the future value of an ordinary annuity formula to find the solution, including specific details and calculations. Suitable for high school students studying finance mathematics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation