If ​$14 comma 000 is invested at 12​% interest compounded monthly​, find the interest earned in 15 years.
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Part 1
The interest earned in 15 years is ​$
  
enter your response here.
​(Do not round until the final answer. Then round to two decimal places as​ needed.)

The formula to calculate the interest earned with compound interest is:

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

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

### Given:
- $ P = 14,000 $
- $ r = 12\% = 0.12 $
- $ n = 12 $ (since interest is compounded monthly)
- $ t = 15 $ years

We first calculate the future value $ A $, and then subtract the principal $ P $ to get the interest earned.

\[
A = 14,000 \left( 1 + \frac{0.12}{12} \right)^{12 \times 15}
\]

Let's calculate that.The interest earned in 15 years is approximately **$69,941.23**.

Would you like more details or have any questions?

Here are 5 related questions to explore further:
1. How does the number of compounding periods per year affect the total interest earned?
2. What would the interest earned be if the interest were compounded quarterly instead of monthly?
3. How would a change in the interest rate to 10% affect the final amount after 15 years?
4. What if the investment period was reduced to 10 years with the same interest rate and compounding period?
5. How does simple interest compare to compound interest for this investment over the same period?

**Tip:** Compound interest grows faster with more frequent compounding periods, such as monthly or daily compounding.

If $14,000 is invested at 12% interest compounded monthly, find the interest earned in 15 years.

Find out how to calculate compound interest for a $14,000 investment at a 12% annual interest rate compounded monthly. This example demonstrates the use of the compound interest formula to calculate the interest earned over 15 years, yielding approximately $69,941.23. Suitable for high school students in Grades 10-12.

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