Bash deposits $2000 in an account earning 2.7% interest compounded daily. How much will Bash have in the account in 1 year?

To find out how much Bash will have in his account after 1 year with daily compounded interest, we can use the compound interest formula:

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

where:
- $ A $ is the amount of money accumulated after $ t $ years, including interest.
- $ P $ is the principal amount (the initial amount of money).
- $ 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.

In this case:
- $ P = 2000 $ dollars
- $ r = 0.027 $ (2.7%)
- $ n = 365 $ (compounded daily)
- $ t = 1 $ year

Let's plug these values into the formula:

\[ A = 2000 \left(1 + \frac{0.027}{365}\right)^{365 \cdot 1} \]

First, calculate the daily interest rate:

\[ \frac{0.027}{365} = 0.00007397 \]

Now, add 1 to the daily interest rate:

\[ 1 + 0.00007397 = 1.00007397 \]

Next, raise this to the power of 365:

\[ 1.00007397^{365} \approx 1.027368 \]

Finally, multiply this by the principal amount:

\[ A = 2000 \times 1.027368 \approx 2054.74 \]

So, Bash will have approximately \$2054.74 in his account after 1 year.

Would you like more details or have any questions about this calculation?

Here are some related questions:
1. How would the amount change if the interest rate were 3% instead of 2.7%?
2. What would the final amount be if the interest was compounded monthly instead of daily?
3. How much interest would Bash earn in 1 year?
4. What is the formula for compound interest?
5. How does the frequency of compounding affect the final amount?
6. What would happen if Bash deposited $2000 for 5 years instead of 1 year?
7. How do you convert an annual interest rate to a daily interest rate?
8. What is the difference between simple interest and compound interest?

**Tip:** Always double-check your calculations to ensure accuracy, especially when dealing with financial formulas and compounding periods.

Learn how to calculate compound interest with daily compounding using the formula A = P (1 + r/n)^(nt). This example solves for the amount Bash will have in his account after 1 year with $2000 deposited at 2.7% interest compounded daily.

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