Use the appropriate compound interest formula to compute the balance in the account after the stated period of time.
​$18 comma 000 is invested for 2 years with an APR of 4.6​% and daily compounding.
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Part 1
The balance in the account after 2 years is ​$
  
19,713.80.
​(Round to the nearest cent as​ needed.)

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.

$18,000 is invested for 2 years with an APR of 4.6% and daily compounding. The balance in the account after 2 years is $19,713.80 (Round to the nearest cent as needed).

Learn how to calculate the balance of an account after 2 years with a principal of $18,000, an APR of 4.6%, and daily compounding. This example covers the use of the compound interest formula and provides a step-by-step solution. Perfect for high school financial math students.

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