Use the compound interest formula to compute the balance in the following account after the stated period of​ time, assuming interest is compounded annually.

​$80008000

invested at an APR of

3.63.6​%

for

1414

years.

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Part 1

The balance in the account after

1414

years is

​$enter your response here.

​(Round to the nearest cent as​ needed.)

The compound interest formula is given by:

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

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

Since the interest is compounded annually, $ n = 1 $. Now, we can input the values:
- $ P = 8000 $
- $ r = 3.6\% = 0.036 $
- $ t = 14 $

The formula becomes:

\[
A = 8000 \left( 1 + \frac{0.036}{1} \right)^{1 \times 14}
\]

Now, let's compute the balance.The balance in the account after 14 years is $13,125.82, rounded to the nearest cent.

Would you like more details or have any questions? Here are some related questions you may find interesting:

1. What would the balance be if the interest were compounded monthly instead of annually?
2. How does the formula change if the investment period is halved?
3. What is the effect of increasing the APR to 5% with the same period?
4. How can we calculate the interest earned over the 14 years?
5. What would be the balance after 14 years if the principal were $10,000 instead of $8,000?

**Tip:** Always convert percentages to decimals when using them in formulas. For example, 3.6% becomes 0.036.

Use the compound interest formula to compute the balance in the following account after the stated period of time, assuming interest is compounded annually. $8000 invested at an APR of 3.6% for 14 years. Round to the nearest cent as needed.

Learn how to calculate the future value of $8000 invested at an APR of 3.6% compounded annually over 14 years using the compound interest formula. This problem covers key algebraic concepts, such as exponential growth and compound interest. Suitable for students in Grades 9-12.

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