Eli deposits $8,000 in Middlesex Savings Bank at an interest rate of 2%, compounded monthly, and leaves it untouched for 3 years.
(a) How much will be in the account in total at the end of the 3 years?

To determine how much will be in Eli's account at the end of 3 years, we will use the formula for compound interest:

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

Where:
- $ A $ is the amount in the account after interest is applied.
- $ P $ is the principal (initial deposit), which is $8,000.
- $ r $ is the annual interest rate (as a decimal), so $ r = 0.02 $.
- $ n $ is the number of times the interest is compounded per year, so $ n = 12 $ (monthly compounding).
- $ t $ is the time the money is invested for, in years, so $ t = 3 $.

Now we substitute the given values into the formula:

\[
A = 8000 \left(1 + \frac{0.02}{12}\right)^{12 \times 3}
\]

I'll calculate this for you.The total amount in Eli's account at the end of 3 years will be approximately **$8,494.27**.

Would you like more details on the calculations or have any other questions?

Here are 5 related questions to further explore:
1. What if the interest was compounded quarterly instead of monthly?
2. How much total interest did Eli earn over the 3 years?
3. How would the total amount change if the interest rate were 3% instead of 2%?
4. How long would it take for the account to grow to $10,000 at the same interest rate?
5. What would the final amount be if Eli deposited $10,000 instead of $8,000?

**Tip:** The more frequently interest is compounded, the faster the investment grows, even at the same annual interest rate.

Eli deposits $8,000 in Middlesex Savings Bank at an interest rate of 2%, compounded monthly, and leaves it untouched for 3 years. (a) How much will be in the account in total at the end of the 3 years?

Learn how to calculate the total amount in an account after depositing $8,000 at a 2% interest rate, compounded monthly, for 3 years. This finance-related problem involves the compound interest formula, making it ideal for high school students (Grades 9-12).

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