You deposit $2000 in an account earning 2% interest compounded monthly. How much will you have in the account in 5 years?

To find out how much you'll have in the account after 5 years with 2% interest compounded monthly, you can use the compound interest formula:

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

Where:
- $ A $ is the amount of money accumulated after $ n $ 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 or borrowed for, in years.

Given:
- $ P = 2000 $ (the principal)
- $ r = 0.02 $ (2% interest rate)
- $ n = 12 $ (compounded monthly)
- $ t = 5 $ years

Now, plug in the values:

\[
A = 2000 \left(1 + \frac{0.02}{12}\right)^{12 \times 5}
\]

First, calculate the monthly interest rate:

\[
\frac{0.02}{12} = 0.0016667
\]

Then calculate the exponent:

\[
12 \times 5 = 60
\]

Now, calculate the amount:

\[
A = 2000 \left(1 + 0.0016667\right)^{60}
\]
\[
A = 2000 \left(1.0016667\right)^{60}
\]

Finally, solve for $ A $:

\[
A \approx 2000 \times 1.104622
\]

\[
A \approx 2209.24
\]

So, after 5 years, you will have approximately **$2209.24** in the account.

Would you like further details on this calculation, or do you have any other questions?

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**Related Questions:**

1. How would the amount change if the interest rate was 3% instead of 2%?
2. What would the final amount be if the interest was compounded quarterly instead of monthly?
3. How much interest would you earn if you kept the money in the account for 10 years?
4. What is the effect of compounding frequency on the final amount?
5. How would the result change if the initial deposit was $5000 instead of $2000?
6. Can you calculate the amount with continuous compounding for the same conditions?
7. How would the amount change if you added $100 every month to the account?
8. What is the difference between simple interest and compound interest for this scenario?

**Tip:** The more frequently the interest is compounded, the more interest you'll accumulate over time.

Learn how to calculate compound interest with monthly compounding. Given a principal of $2000, an interest rate of 2% compounded monthly over 5 years, find out the accumulated amount using the compound interest formula. Detailed step-by-step solution provided.

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