On August 27th, 2013, Joseph invested $16,000 in a fund that was growing at 6% compounded quarterly.
Calculate the future value of the fund on March 18th, 2014.


To calculate the future value of Joseph's investment, we need to apply the formula for compound interest:

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

Where:
- $A$ is the future value of the investment.
- $P = 16,000$ is the principal (initial investment).
- $r = 0.06$ is the annual interest rate (6% expressed as a decimal).
- $n = 4$ is the number of compounding periods per year (since it's compounded quarterly).
- $t$ is the time in years.

### Step 1: Determine the time period ($t$)
Joseph invested the money on August 27, 2013, and we're calculating the future value on March 18, 2014. To calculate the time difference:

- From August 27, 2013, to March 18, 2014, there are 203 days.
- The number of years is $ t = \frac{203}{365} \approx 0.5562 $.

### Step 2: Apply the compound interest formula
Now that we have all the values, substitute them into the formula:

\[
A = 16,000 \left(1 + \frac{0.06}{4}\right)^{4 \times 0.5562}
\]

I'll calculate this value next.The future value of Joseph's investment on March 18, 2014, is approximately **$16,538.83**.

Would you like more details, or have any further questions?

Here are 5 related questions to expand this topic:
1. How would the future value change if the interest rate were compounded monthly?
2. What would the future value be after 1 year of investment?
3. How does changing the compounding frequency affect the future value?
4. How long would it take for the investment to double at a 6% annual interest rate compounded quarterly?
5. What if Joseph had withdrawn part of the money midway through the investment period?

**Tip**: Always double-check the time periods and compounding frequency when calculating compound interest; small changes can have a notable effect.

On August 27th, 2013, Joseph invested $16,000 in a fund that was growing at 6% compounded quarterly. Calculate the future value of the fund on March 18th, 2014.

Find out how to calculate the future value of a $16,000 investment at 6% interest compounded quarterly over 203 days. This example explains the use of the compound interest formula and covers essential financial math concepts. Suitable for high school students (Grades 10-12).

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