Find the compound amount for the deposit and the amount of interest earned.
​$15,000 at 7​% compounded monthly for 13 years. The compound amount after 13 years is

To find the compound amount, we can use the compound interest formula:

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

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

In this problem:
- $ P = 15,000 $
- $ r = 7\% = 0.07 $
- $ n = 12 $ (since interest is compounded monthly)
- $ t = 13 $ years.

### Step 1: Plug the values into the formula:

\[
A = 15,000 \left(1 + \frac{0.07}{12}\right)^{12 \times 13}
\]

\[
A = 15,000 \left(1 + 0.0058333\right)^{156}
\]

\[
A = 15,000 \left(1.0058333\right)^{156}
\]

Now, I'll calculate the compound amount.The compound amount after 13 years is approximately **$37,166.44**.

### Step 2: Calculate the interest earned:
The interest earned is the difference between the compound amount and the initial principal:

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

\[
\text{Interest} = 37,166.44 - 15,000 = 22,166.44
\]

So, the interest earned is approximately **$22,166.44**.

Would you like more details or have any questions about this?

### Related Questions:
1. How does changing the compounding frequency affect the compound amount?
2. What is the difference between simple and compound interest in this scenario?
3. How would the compound amount change if the interest rate were 8% instead of 7%?
4. What if the compounding was done annually instead of monthly?
5. How much would the interest be if the deposit was left for 20 years instead of 13?

### Tip:
When calculating compound interest, increasing the frequency of compounding (e.g., monthly vs. annually) increases the total amount earned due to more frequent interest applications.

Find the compound amount for the deposit and the amount of interest earned. $15,000 at 7% compounded monthly for 13 years. The compound amount after 13 years is?

Calculate the compound interest for a $15,000 deposit at 7% compounded monthly over 13 years. Learn how the formula A = P(1 + r/n)^(nt) is applied to determine the total compound amount ($37,166.44) and interest earned ($22,166.44). Suitable for students in Grades 10-12.

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