A savings account starts with $500. After each year, it grows by 1.3%. What is the account worth after 15 years?

To find the future value of the savings account, we use the formula for compound interest:

\[
A = P \times (1 + r)^n
\]

where:
- $ A $ is the amount of money accumulated after n years, including interest.
- $ P $ is the principal amount (initial sum of money).
- $ r $ is the annual interest rate (decimal).
- $ n $ is the number of years the money is invested for.

Given:
- $ P = 500 $ dollars
- $ r = 1.3\% = 0.013 $
- $ n = 15 $ years

Now, plug in the values:

\[
A = 500 \times (1 + 0.013)^{15}
\]

\[
A = 500 \times (1.013)^{15}
\]

Calculating $ (1.013)^{15} $:

\[
(1.013)^{15} \approx 1.209
\]

Then,

\[
A \approx 500 \times 1.209 = 604.50
\]

Therefore, the account will be worth approximately $604.50 after 15 years.

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

Here are 5 related questions:
1. How would the result change if the interest rate was 2% instead of 1.3%?
2. What would be the final amount if the initial deposit was $1,000?
3. How much interest is earned over the 15 years?
4. What would the account value be after 10 years instead of 15?
5. How does compound interest differ from simple interest in this scenario?

**Tip:** Always convert percentage rates to decimals when using them in calculations by dividing by 100.

Learn how to calculate the future value of a savings account starting with $500 and growing by 1.3% annually over 15 years. This detailed solution demonstrates the use of the compound interest formula, showing step-by-step calculations for exponential growth. Ideal for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation