Eva invests $7900 in a new savings account which earns 4.9% annual interest, compounded quarterly.  What will be the value of her investment after 7 years?  Round to the nearest cent.

To find the future value of Eva's investment, we can use the compound interest formula:

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

Where:
- $A$ is the amount of the investment after $t$ years.
- $P$ is the principal amount (initial investment).
- $r$ is the annual interest rate (decimal).
- $n$ is the number of times the interest is compounded per year.
- $t$ is the time the money is invested for in years.

Given:
- $P = 7900$
- $r = 4.9\% = 0.049$
- $n = 4$ (compounded quarterly)
- $t = 7$ years

Now, substituting the values into the formula:

\[
A = 7900 \left( 1 + \frac{0.049}{4} \right)^{4 \times 7}
\]

Let's calculate this step by step.The value of Eva's investment after 7 years will be \$11,109.26, rounded to the nearest cent.

Would you like further details or have any other questions?

Here are 5 related questions you might find useful:
1. How does quarterly compounding affect interest growth compared to annual compounding?
2. What if the interest rate was compounded monthly instead of quarterly?
3. How would the investment value change if the interest rate was higher, say 6%?
4. What is the difference between simple interest and compound interest for the same principal?
5. How can Eva calculate how much interest she earned after 7 years?

**Tip:** The more frequently interest is compounded, the greater the return due to the effect of earning "interest on interest" more often.

Eva invests $7900 in a new savings account which earns 4.9% annual interest, compounded quarterly. What will be the value of her investment after 7 years? Round to the nearest cent.

Discover how to calculate the future value of Eva's $7900 investment with a 4.9% annual interest rate compounded quarterly over 7 years. This problem uses the compound interest formula and demonstrates how interest grows exponentially. Suitable 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