You have just started a new job and plan to save $5,400 per year for 32 years until you retire. You will make your first deposit in one year. How much will you have when you retire if you earn an annual interest rate of 9.26 percent?

Multiple Choice

$891,711.95

$893,153.87

$901,553.44

$933,751.77

$849,672.13

This problem involves calculating the future value of an ordinary annuity because you are depositing a fixed amount ($5,400) annually for 32 years, with an interest rate of 9.26% compounded annually.

The future value $ FV $ of an ordinary annuity is given by the formula:

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

Where:
- $ P $ = annual payment = $5,400
- $ r $ = interest rate per period = 9.26% = 0.0926
- $ n $ = number of periods = 32 years

Now, let's compute this.The future value of your savings when you retire is approximately **$933,751.77**.

Therefore, the correct answer is:

**$933,751.77**

Would you like further details on the calculation or have any questions?

Here are five related questions to expand your understanding:
1. What happens if you make deposits at the beginning of each year instead of the end?
2. How would the total savings change if the interest rate were lower, say 7%?
3. How does the future value change if the number of years is reduced to 25 years?
4. What is the difference between an ordinary annuity and an annuity due?
5. How does compounding frequency (e.g., monthly vs. annually) affect the future value?

**Tip**: Increasing the interest rate, even by a small percentage, can significantly impact the future value of long-term investments due to the power of compound interest.

You have just started a new job and plan to save $5,400 per year for 32 years until you retire. You will make your first deposit in one year. How much will you have when you retire if you earn an annual interest rate of 9.26 percent?

Learn how to calculate the future value of an ordinary annuity with fixed annual payments of $5,400 for 32 years at an annual interest rate of 9.26%. This example covers key financial concepts such as compound interest and ordinary annuities, making it suitable for students in Grades 11-12 or introductory college courses.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation