Suppose that you invest $24,000 in an account that earns interest at an APR of 2.9%, compounded monthly. Determine the accumulated balance after 10 years.

$32,331.16

$32,062.40

$31,968.02

$32,063.04

None of the above.

To determine the accumulated balance after 10 years in an account with a principal of $24,000, an annual percentage rate (APR) of 2.9%, and monthly compounding, we'll use the formula for compound interest:

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

Where:
- $A$ is the accumulated balance after $t$ years.
- $P$ is the principal amount (initial investment), which is $24,000.
- $r$ is the annual interest rate (as a decimal), so 2.9% becomes 0.029.
- $n$ is the number of times the interest is compounded per year, which is 12 (monthly).
- $t$ is the time in years, which is 10 years.

Substituting the given values:

\[
A = 24000 \left(1 + \frac{0.029}{12}\right)^{12 \times 10}
\]

Now let's calculate the accumulated balance.The accumulated balance after 10 years is approximately **$32,063.04**. 

So, the correct answer is **$32,063.04**.

Would you like further details or have any other questions?

Here are five related questions you might find interesting:
1. How would the accumulated balance change if the interest rate were 3.5% instead of 2.9%?
2. What would the accumulated balance be after 15 years with the same interest rate and principal?
3. How does increasing the compounding frequency (e.g., daily compounding) affect the final balance?
4. What is the difference between simple interest and compound interest?
5. How much would you need to invest initially to reach $40,000 in 10 years at the same APR?

**Tip:** Compounding more frequently results in a higher accumulated balance, as interest is calculated and added more often.

Suppose that you invest $24,000 in an account that earns interest at an APR of 2.9%, compounded monthly. Determine the accumulated balance after 10 years.

$32,331.16
$32,062.40
$31,968.02
$32,063.04
None of the above.

Discover how to calculate the accumulated balance for an investment of $24,000 at an APR of 2.9% compounded monthly over 10 years. This problem uses the compound interest formula and covers essential algebraic and financial concepts. Suitable for Grades 9-12 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation