Suppose that  $3,500
  is invested at  5.2%
  compounded quarterly. How much money will be in the account in  19
  years? Round your final answer to the nearest cent. Do not round until final answe

To solve this, we use the formula for compound interest:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $A$ is the amount of money in the account after $t$ years
- $P$ is the initial principal (in this case, $P = 3500$)
- $r$ is the annual interest rate (as a decimal, $r = 0.052$)
- $n$ is the number of times the interest is compounded per year (since it’s compounded quarterly, $n = 4$)
- $t$ is the number of years (in this case, $t = 19$)

Now we can plug the given values into the formula:

\[
A = 3500 \left(1 + \frac{0.052}{4}\right)^{4 \times 19}
\]

I'll calculate the value for $A$.The amount of money in the account after 19 years will be **$9,340.84**.

Would you like more details or explanations on any part of this solution?

Here are 5 related questions to consider:
1. What if the interest was compounded monthly instead of quarterly?
2. How would the final amount change if the interest rate was 6%?
3. What is the total interest earned over the 19 years?
4. How long would it take to double the investment at the same rate?
5. How would the calculation change if the initial principal was $5,000?

**Tip**: Always double-check the number of compounding periods ($n$) to ensure accurate calculations when working with compound interest formulas!

Suppose that $3,500 is invested at 5.2% compounded quarterly. How much money will be in the account in 19 years? Round your final answer to the nearest cent.

Learn how to calculate the future value of an investment of $3,500 at a 5.2% interest rate compounded quarterly over 19 years. Using the compound interest formula, this solution provides a detailed step-by-step approach, 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