The present value formula used for compound interest is given by:

$PV = \frac{FV}{(1 + \frac{r}{n})^{nt}}$

Where:

• $PV$ = present value (how much you need to invest now),
• $FV$ = future value (the amount you want in the future, $11,000),
• $r$ = annual interest rate (6% or 0.06),
• $n$ = number of times the interest is compounded per year (semiannually, so $n = 2$),
• $t$ = time in years (15 years).

Let's substitute the values into the formula and calculate:

$PV = \frac{11,000}{(1 + \frac{0.06}{2})^{2 \times 15}}$

Now, let me compute this for you.The correct amount you should invest now is approximately $4,531.85 in order to have $11,000 in 15 years with a 6% interest rate compounded semiannually.

Would you like further details or explanations on any part of the process?

Here are 5 related questions:

1. How would the investment amount change if the interest rate were higher?
2. What happens if the interest is compounded quarterly instead of semiannually?
3. How does the future value change if you extend the investment period by 5 more years?
4. What would the formula be if the interest was compounded continuously?
5. How much interest would you earn after 15 years with this initial investment?

Tip: The more frequently interest is compounded, the more your investment grows due to the effect of compound interest.