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To solve this problem, we will use the formula for compound interest:

\[
FV = PV \times \left(1 + \frac{r}{n}\right)^{n \cdot t}
\]

Where:
- $ FV $ = future value (the amount we want to find)
- $ PV $ = present value (initial investment), which is $10,000
- $ r $ = annual interest rate, which is 1.5% or 0.015 in decimal form
- $ n $ = number of times the interest is compounded per year, which is 4 (quarterly compounding)
- $ t $ = number of years, which is 3

### Step-by-Step Calculation:

1. Convert the interest rate to decimal form: $ r = 0.015 $.
2. Substitute the values into the formula:

\[
FV = 10000 \times \left(1 + \frac{0.015}{4}\right)^{4 \times 3}
\]

3. Calculate the value inside the parentheses:

\[
1 + \frac{0.015}{4} = 1 + 0.00375 = 1.00375
\]

4. Raise this result to the power of $4 \times 3 = 12$:

\[
1.00375^{12} \approx 1.0458
\]

5. Multiply by the initial amount:

\[
FV = 10000 \times 1.0458 \approx 10458
\]

### Answer:
The future value $ FV $ is approximately **$10,458.00**.

Would you like further details or have any questions?

### Related Questions:

1. How would the future value change if compounded annually instead of quarterly?
2. What would be the future value after 5 years with the same interest rate and compounding frequency?
3. How does increasing the interest rate to 2% affect the future value after 3 years?
4. How is compound interest different from simple interest for the same investment?
5. How does changing the compounding frequency to monthly impact the future value?

### Tip:
In compound interest, increasing the frequency of compounding (e.g., from annually to quarterly or monthly) increases the future value of the investment due to interest being added more frequently.

Calculate, to the nearest cent, the future value (FV in dollars) of an investment of $10,000 at 1.5% per year, compounded quarterly (4 times/year), after 3 years.

Find the future value of a $10,000 investment at a 1.5% annual interest rate, compounded quarterly, over a 3-year period. This calculation uses the compound interest formula and covers concepts like exponential growth and quarterly compounding.

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