On June 27th, 2013, Joseph invested $17,000 in a fund that was growing at 6% compounded quarterly.

**a.** Calculate the future value of the fund on January 27th, 2014.

To calculate the future value of the fund on January 27th, 2014, we can use the formula for compound interest:

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

Where:
- $A$ is the future value (the amount after interest has been applied),
- $P$ is the principal (the initial investment),
- $r$ is the annual interest rate (expressed as a decimal),
- $n$ is the number of times the interest is compounded per year,
- $t$ is the time in years.

### Given information:
- $P = 17,000$ (initial investment),
- $r = 0.06$ (6% annual interest rate),
- $n = 4$ (since the interest is compounded quarterly),
- $t$ is the time from June 27th, 2013 to January 27th, 2014, which is 7 months or $\frac{7}{12}$ years.

Now, let's calculate the future value.The future value of the fund on January 27th, 2014, is approximately **$17,600.96**.

Would you like further details on the calculation or have any questions?

Here are five related questions for further exploration:
1. What would the future value be if the investment period were 1 year instead of 7 months?
2. How would the future value change if the interest were compounded monthly instead of quarterly?
3. What is the total interest earned during this 7-month period?
4. How would the result differ if the interest rate were 8% instead of 6%?
5. How can you calculate the effective annual rate (EAR) from the given compounded quarterly rate?

**Tip:** To calculate interest over different compounding periods, adjust the value of $n$ in the compound interest formula accordingly.

On June 27th, 2013, Joseph invested $17,000 in a fund that was growing at 6% compounded quarterly. Calculate the future value of the fund on January 27th, 2014.

Learn how to calculate the future value of a $17,000 investment with a 6% interest rate compounded quarterly over a 7-month period. This example uses the compound interest formula and demonstrates exponential growth for high school math students (Grades 9-12).

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