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This problem involves compound interest with quarterly compounding. We will use the compound interest formula:

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

Where:
- $ A $ = the amount of money after interest
- $ P $ = the principal (initial investment), which is \$1500
- $ r $ = the annual interest rate (1.11% = 0.0111)
- $ n $ = the number of times the interest is compounded per year (quarterly, so $ n = 4 $)
- $ t $ = the number of years (2 years)

### (a) How much money is in Manuel's account after 2 years?

We will calculate the future value of the investment using the values above.

### (b) How much interest is earned after 2 years?

The interest earned is simply the final amount minus the principal:
\[
\text{Interest} = A - P
\]

Let me calculate both of these.### (a) The total amount in Manuel's account after 2 years is approximately **$1533.63**.

### (b) The interest earned after 2 years is approximately **$33.63**.

Would you like any further details or clarification?

Here are 5 related questions you might find helpful:
1. How does increasing the compounding frequency affect the final amount?
2. What would happen if the interest rate increased to 2%?
3. How would the amount change if Manuel invested for 5 years instead of 2?
4. How can you calculate the interest earned if compounding is done monthly instead of quarterly?
5. How does simple interest differ from compound interest?

**Tip:** Always check if the interest is compounded annually, quarterly, monthly, etc., as it significantly affects the total amount.

Manuel received a $1500 bonus. He decided to invest it in a 2-year certificate of deposit (CD) with an annual interest rate of 1.11% compounded quarterly. How much money will be in his account after 2 years, and how much interest is earned?

Learn how to calculate the final amount and interest earned from a $1500 investment over 2 years with a 1.11% annual interest rate compounded quarterly. Understand the key concepts of compound interest and use the formula A = P(1 + r/n)^(nt).

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