
Suppose you deposit $7000 into an account that earns 6.7 interest compounded quarterly compute the amount of money in the account after 11 years how much of that is interest?

To calculate the amount of money in the account after 11 years with interest compounded quarterly, we'll use the formula for compound interest:

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

Where:
- $ A $ is the amount of money accumulated after $ n $ years, including interest.
- $ P $ is the principal amount (the initial amount of money) = \$7,000.
- $ r $ is the annual interest rate (decimal) = 6.7\% or 0.067.
- $ n $ is the number of times that interest is compounded per year = 4 (since it's compounded quarterly).
- $ t $ is the time the money is invested for, in years = 11 years.

### Step 1: Calculate the amount $ A $:

\[
A = 7000 \left(1 + \frac{0.067}{4}\right)^{4 \times 11}
\]

### Step 2: Calculate the interest earned.

The interest earned is the total amount $ A $ minus the principal $ P $:

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

I'll calculate this now.After 11 years, the amount of money in the account will be **$14,538.58**.

Out of that amount, **$7,538.58** is interest earned.

Would you like any more details, or do you have any questions?

### Here are 5 follow-up questions related to this problem:

1. What if the interest rate was compounded monthly instead of quarterly?
2. How much would you have after 15 years instead of 11 years?
3. What would be the impact of increasing the interest rate to 8%?
4. How would the amount change if you deposited an additional $1000 after 5 years?
5. What would happen if the interest was compounded continuously?

**Tip:** When comparing different savings or investment accounts, always check how often the interest is compounded, as more frequent compounding leads to more interest earned.

Learn how to calculate compound interest after 11 years on a $7000 deposit with an annual interest rate of 6.7% compounded quarterly. The total amount and interest earned are computed using the compound interest formula. Explore variations such as monthly compounding and increased interest rates.

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