https://file.aiquickdraw.com/mathbot/file/17278406859977wzdbock.jpg

To find the future value of an annuity with the given parameters, we will use the **future value of an ordinary annuity formula**:

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

Where:
- $ P $ is the payment amount per period ($1900),
- $ r $ is the interest rate per period (6% = 0.06),
- $ n $ is the number of periods (5 years).

Let's calculate it step by step:

\[
FV = 1900 \times \left( \frac{(1 + 0.06)^5 - 1}{0.06} \right)
\]

First, calculate $ (1 + 0.06)^5 $:

\[
(1.06)^5 = 1.338225
\]

Next, subtract 1 from this result:

\[
1.338225 - 1 = 0.338225
\]

Now, divide by 0.06:

\[
\frac{0.338225}{0.06} = 5.637083
\]

Finally, multiply by the payment amount, $1900:

\[
FV = 1900 \times 5.637083 = 10,710.46
\]

The future value of the annuity is approximately **$10,710.46**.

Would you like further details on this, or have any additional questions?

Here are 5 related questions:
1. What is the difference between an ordinary annuity and an annuity due?
2. How would the future value change if payments were made at the beginning of each period?
3. How would the future value be impacted if the interest rate were compounded monthly instead of annually?
4. What would happen to the future value if the payment amount increased each year?
5. How do you calculate the present value of an annuity?

**Tip**: When calculating annuity values, remember that the timing of payments (end or beginning of periods) significantly affects the result.

Find the future value of an annuity of $1900 paid at the end of each year for 5 years, if interest is earned at a rate of 6%, compounded annually.

Learn how to calculate the future value of an annuity of $1900 paid annually for 5 years, with a 6% annual interest rate. This problem involves key financial concepts, such as compound interest and the future value of annuities, and is suitable for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation