To calculate the balance of an account using the compound interest formula, you can use the following equation:

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

Where:

• $A$ is the amount of money in the account after interest (the final balance).
• $P$ is the initial principal (the amount of money initially invested).
• $r$ is the annual percentage rate (APR) as a decimal.
• $n$ is the number of times the interest is compounded per year.
• $t$ is the number of years the money is invested.

Given dataTo calculate the balance of an account using the compound interest formula, you can use the following equation:

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

Where:

• $A$ is the amount of money in the account after interest (the final balance).
• $P$ is the initial principal (the amount of money initially invested).
• $r$ is the annual percentage rate (APR) as a decimal.
• $n$ is the number of times the interest is compounded per year.
• $t$ is the number of years the money is invested.

Given

• $P = 18,000$
• $r = 4.6\% = 0.046$
• $n = 365$ (since the interest is compounded daily)
• $t = 2$ years

Now, substituting these values into the formula:

$A = 18,000 \left( 1 + \frac{0.046}{365} \right)^{365 \times 2}$

I'll calculate that for you.The balance in the account after 2 years, with daily compounding at an APR of 4.6%, is approximately $19,734.45.

Would you like further details on the calculation or have any other questions?

Here are five related questions you might find interesting:

1. How does the balance change if the compounding frequency is monthly instead of daily?
2. What happens if the investment is extended to 5 years?
3. How does the APR affect the final balance if it is increased to 6%?
4. What is the effect of compounding interest semi-annually versus daily?
5. How would the result differ if simple interest were applied instead of compound interest?

Tip: The more frequently interest is compounded, the higher the final balance will be due to the effect of earning interest on interest.