https://file.aiquickdraw.com/mathbot/file/1726663058491zolb20ek.jpg

To solve this problem, we need to use the formula for compound interest to find both the future value of the investment and the interest earned after 2 years.

The formula for compound interest is:

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

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

### Given:
- $P = 3500$ (Joe's initial investment).
- $r = 0.0124$ (1.24% interest rate).
- $n = 1$ (interest is compounded annually).
- $t = 2$ years.

#### Step 1: Calculate the future value $A$.
Substitute the given values into the formula:

\[
A = 3500 \left(1 + \frac{0.0124}{1}\right)^{1 \times 2}
\]

#### Step 2: Find the interest earned.
The interest earned is simply the difference between the future value $A$ and the initial investment $P$.

\[
\text{Interest} = A - P
\]

Let me calculate these values for you.### Results:
(a) The amount of money in Joe's account after 2 years is approximately **$3587.34**.

(b) The interest earned on Joe's investment after 2 years is approximately **$87.34**.

Do you have any questions or would you like more details? 

Here are some related questions:
1. How would the future value change if the interest rate were 2% instead of 1.24%?
2. What happens if the investment is compounded monthly instead of annually?
3. How much would Joe earn if he invested for 5 years at the same rate?
4. What is the total interest earned if Joe made an additional deposit of $1000 after the first year?
5. How does compound interest differ from simple interest in terms of earnings?

**Tip:** Compound interest grows faster when interest is compounded more frequently (e.g., monthly or daily).

A bank offers an investment account with an annual interest rate of 1.24% compounded annually. Joe invests $3500 into the account for 2 years. (a) How much money is in Joe's account after 2 years? (b) How much interest is earned on Joe's investment after 2 years?

Learn how to calculate compound interest for an investment account. Joe invests $3500 at an interest rate of 1.24%, compounded annually for 2 years. Find the total amount in Joe's account and the interest earned after 2 years. Ideal for high school students learning about compound interest.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation