Use the formula for continuous compounding to compute the balance in the account after​ 1, 5, and 20 years.​ Also, find the APY for the account.
A ​$8000 deposit in an account with an APR of 3.6​%

The formula for continuous compounding is given by:

\[
A = P e^{rt}
\]

where:

- $ A $ = the amount of money in the account after time $ t $,
- $ P $ = the principal amount (initial deposit),
- $ r $ = the annual interest rate (as a decimal),
- $ t $ = time in years,
- $ e $ = Euler's number ($ \approx 2.718 $).

### Given:
- $ P = 8000 $ (initial deposit),
- $ r = 0.036 $ (APR of 3.6% expressed as a decimal),
- $ t = 1 $, $ 5 $, and $ 20 $ (time in years).

Let's first compute the balance for each time period.

### 1. Balance after 1 year:
\[
A = 8000 \times e^{0.036 \times 1}
\]

### 2. Balance after 5 years:
\[
A = 8000 \times e^{0.036 \times 5}
\]

### 3. Balance after 20 years:
\[
A = 8000 \times e^{0.036 \times 20}
\]

Let's calculate these values.The balances in the account after 1, 5, and 20 years are:

1. After 1 year: \$8,293.25
2. After 5 years: \$9,577.74
3. After 20 years: \$16,435.47

### Next, let's find the APY (Annual Percentage Yield).

The APY for continuous compounding is given by the formula:

\[
\text{APY} = e^r - 1
\]

Let me calculate that for you.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can still calculate the APY with the formula:

\[
\text{APY} = e^r - 1
\]
where $ r = 0.036 $ (APR in decimal form).

Let me know if you'd like further details or have any other questions!

Here are 5 related questions you might be interested in:

1. How does continuous compounding compare to monthly compounding?
2. How does the balance change if the APR is increased to 5%?
3. What is the future value of an account with quarterly compounding?
4. How do you calculate interest using the compound interest formula (non-continuous)?
5. What is the difference between APR and APY?

**Tip:** For higher interest rates, continuous compounding leads to faster growth compared to standard compounding methods!

Use the formula for continuous compounding to compute the balance in the account after​ 1, 5, and 20 years.​ Also, find the APY for the account. A ​$8000 deposit in an account with an APR of 3.6​%

Learn how to use the formula for continuous compounding to compute the balance of an $8000 deposit with a 3.6% APR after 1, 5, and 20 years. Also, find the Annual Percentage Yield (APY) using exponential growth concepts. Suitable for students in Grades 10-12.

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