The following money market account rates were available from a particular bank. Find the compound amount and the interest earned.
​$16 comma 000 at 1.04​% compounded monthly for three years
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Part 1
The compound amount is ​$
  
enter your response here.
​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

To solve this problem, we'll use the compound interest formula:

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

Where:
- $A$ = the compound amount (the final amount)
- $P$ = the principal (initial investment), which is $16,000
- $r$ = annual interest rate (expressed as a decimal), which is 1.04% or 0.0104
- $n$ = number of times the interest is compounded per year, which is monthly (12 times per year)
- $t$ = the number of years, which is 3 years

Let's plug the numbers into the formula:

\[
A = 16,000 \left(1 + \frac{0.0104}{12}\right)^{12 \times 3}
\]

First, calculate the term inside the parentheses:

\[
1 + \frac{0.0104}{12} = 1 + 0.0008667 = 1.0008667
\]

Now, raise it to the power of $12 \times 3 = 36$:

\[
1.0008667^{36} \approx 1.031557
\]

Now multiply by the principal $P = 16,000$:

\[
A = 16,000 \times 1.031557 \approx 16,504.91
\]

So, the compound amount is approximately **$16,504.91**.

### Part 2: Interest earned
To find the interest earned, subtract the initial principal from the compound amount:

\[
\text{Interest} = A - P = 16,504.91 - 16,000 = 504.91
\]

The interest earned is approximately **$504.91**.

Would you like more details or have any questions?

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Here are 5 related questions:
1. How does increasing the interest rate affect the compound amount?
2. What happens if the compounding frequency is changed to quarterly?
3. Can you explain the difference between simple interest and compound interest?
4. What if the investment period was extended to 5 years—what would be the new compound amount?
5. How would daily compounding impact the interest earned?

**Tip:** The more frequently interest is compounded, the higher the final amount will be!

The following money market account rates were available from a particular bank. Find the compound amount and the interest earned. ​$16,000 at 1.04% compounded monthly for three years.

Learn how to calculate the compound amount and interest earned on a $16,000 investment at 1.04% compounded monthly over 3 years. This example uses the compound interest formula to demonstrate step-by-step financial mathematics. Perfect for high school students (Grades 10-12).

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