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!