If $20,000 is invested in an account for 15 years. Calculate the total interest earned at the end of 15 years if the interest is:  7% compounded annually:

To calculate the total interest earned on an investment with compounded interest, we can use the compound interest formula:

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

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

In this case:
- $ P = 20,000 $
- $ r = 7\% = 0.07 $
- $ n = 1 $ (since it is compounded annually)
- $ t = 15 $ years

### Step 1: Calculate the future value ($ A $)
\[
A = 20000 \left(1 + \frac{0.07}{1}\right)^{1 \times 15}
\]
\[
A = 20000 \left(1 + 0.07\right)^{15}
\]
\[
A = 20000 \times (1.07)^{15}
\]

Now, let me calculate this.The future value of the investment after 15 years is approximately $ A = 55,180.63 $.

### Step 2: Calculate the total interest earned
The total interest earned is the difference between the future value ($ A $) and the initial principal ($ P $):

\[
\text{Interest} = A - P = 55,180.63 - 20,000 = 35,180.63
\]

Thus, the total interest earned after 15 years is approximately **$35,180.63**.

Do you want more details or have any other questions?

Here are 5 related questions for further practice:
1. What if the interest were compounded quarterly instead of annually?
2. How much would be earned if the interest rate were 5% instead of 7%?
3. How much total interest would be earned after 10 years instead of 15?
4. What would the total amount be if $30,000 were invested instead of $20,000?
5. What is the total interest if the interest were compounded monthly?

**Tip**: Compound interest grows faster than simple interest because the interest is calculated on both the initial principal and the accumulated interest from previous periods.

If $20,000 is invested in an account for 15 years. Calculate the total interest earned at the end of 15 years if the interest is: 7% compounded annually.

Learn how to calculate the total interest earned on a $20,000 investment at 7% compounded annually over 15 years. This problem covers key financial concepts like compound interest and exponential growth, with a detailed step-by-step solution. Suitable for Grades 9-12 students.

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