Danielle has a CD at Crossland Bank. She invests $22,350 for four years at 1.55% interest, compounded monthly. How much interest did she make?

To determine how much interest Danielle made on her investment, we can use the compound interest formula:

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

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

Given:
- $ P = 22,350 $
- $ r = 1.55\% = 0.0155 $
- $ t = 4 $ years
- $ n = 12 $ (since the interest is compounded monthly)

First, let's calculate $ A $, the total amount after 4 years. Then, we can subtract the initial principal $ P $ to find the interest earned.

\[
A = 22,350 \left(1 + \frac{0.0155}{12}\right)^{12 \times 4}
\]

Let's calculate this.After 4 years, Danielle's investment grows to approximately $23,778.61. The interest she earns on her initial investment is about **$1,428.61**.

Would you like more details or have any questions?

Here are 5 related questions to expand on this:

1. What would happen if the interest rate increased to 2%?
2. How much interest would Danielle earn if the investment period was 5 years?
3. What would the total be if the interest was compounded quarterly instead of monthly?
4. How does simple interest compare to compound interest in this scenario?
5. What if Danielle added $500 every year to her investment?

**Tip:** The more frequently interest is compounded, the higher the total interest earned. Monthly compounding generates more interest than annual or quarterly compounding.

Learn how to calculate the compound interest on an investment of $22,350 at 1.55% interest, compounded monthly for 4 years. This problem uses the compound interest formula and covers essential concepts in exponential growth. Suitable for high school students (Grades 10-12).

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