https://file.aiquickdraw.com/mathbot/file/1726784052413bnp4ghnm.jpg

The problem in the image is about calculating the future value of an annuity, given the following parameters:

- Tony invests $1233 every year.
- The interest rate is 6.3%, compounded annually.
- The duration of the investment is 19 years.

The formula for the future value of an ordinary annuity (where payments are made at the end of each period) is:

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

Where:
- $ FV $ is the future value of the annuity.
- $ P $ is the annual payment (\$1233 in this case).
- $ r $ is the annual interest rate (6.3% or 0.063).
- $ n $ is the number of periods (19 years).

Let's calculate it now.The total future value of the annuity after 19 years, with an annual payment of $1233 and a 6.3% interest rate compounded annually, is approximately **$42,910.52**.

The value you provided in the image (**$47,929.20**) seems to differ, suggesting a possible calculation or rounding issue elsewhere. 

Would you like more details on how this was calculated, or have any other questions?

Here are some related questions to expand on this:
1. How would the future value change if the interest rate were compounded monthly instead of annually?
2. What is the effect of increasing the investment duration from 19 years to 25 years?
3. How much would the future value decrease if the interest rate was only 5% instead of 6.3%?
4. What would be the total interest earned over the 19-year period?
5. How does the future value differ between an ordinary annuity and an annuity due (where payments are made at the beginning of each year)?

**Tip:** Be careful with rounding during intermediate steps when calculating annuities, as it can lead to different final results.

To save money for his daughter's college tuition, Tony invests $1233 every year in an annuity that pays 6.3% interest, compounded annually. Payments will be made at the end of each year. Find the total value of the annuity in 19 years.

Learn how to calculate the future value of an annuity where $1233 is invested annually at 6.3% interest, compounded annually, over 19 years. This problem demonstrates how to apply the future value formula for annuities and compound interest concepts, suitable for Grades 10-12 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation