You start saving $1,000 at the end of this year and increase your saving by 8% every year for 19 years.  Your account earns 10%.  How much will you have in your account in 19 years?



This problem involves calculating the future value of a growing annuity, where both the savings amount and the interest rate increase over time.

Here’s a step-by-step explanation of how to calculate the future value of such a series of payments:

### Key information:
- **Initial savings**: $1,000
- **Growth rate of savings**: 8% annually
- **Annual interest rate**: 10%
- **Time period**: 19 years

### Formula:
The future value $ FV $ of a growing annuity is given by the formula:

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

Where:
- $ P $ is the initial payment (in this case, $1,000)
- $ r $ is the interest rate (10% or 0.10)
- $ g $ is the growth rate of the savings (8% or 0.08)
- $ n $ is the number of years (19 years)

Let’s plug in the values and compute it.The future value of your savings after 19 years will be approximately **$90,010.40**.

Would you like a detailed breakdown of the calculations or any further clarifications?

Here are 5 related questions that might expand your understanding:
1. How would the future value change if the interest rate were lower (e.g., 8%)?
2. What happens to the future value if the savings growth rate increases to 10%?
3. How can you calculate the total amount of money saved without considering interest?
4. What would be the future value if the initial savings amount were $1,500?
5. How does the future value change if you save at the beginning of each year instead of the end?

**Tip:** The earlier you start saving, the more compound interest will work in your favor, especially with increasing contributions!

You start saving $1,000 at the end of this year and increase your saving by 8% every year for 19 years. Your account earns 10%. How much will you have in your account in 19 years?

Learn how to calculate the future value of a growing annuity where initial savings are $1,000, increasing by 8% annually, and earning 10% interest over 19 years. This step-by-step guide covers essential finance concepts like compound interest and annuity growth. Suitable for advanced high school students and college-level learners.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation