Pinnacle Homes, a real estate development company, is planning to build five homes, each costing $125,000, in 2.5 years. The Galaxy Bank pays 6% interest compounded semiannually. How much should the company invest now to have sufficient funds to build the homes in the future?

107826.25

PV = 125000(1.03)^-5

= $107,826.10

539131.25

None of these are right.

To calculate the amount the company should invest now, we need to determine the future value of the five homes in 2.5 years, taking into account the interest earned at a rate of 6% compounded semiannually.

The formula to calculate the future value of an investment with compound interest is:

FV = PV(1 + r/n)^(nt)

Where:
FV = Future Value
PV = Present Value (the initial investment)
r = Interest rate per compounding period (in decimal form)
n = Number of compounding periods per year
t = Number of years

In this case:
PV = ?
FV = 5 homes * $125,000 per home
r = 6% per year = 0.06
n = 2 (since interest is compounded semiannually)
t = 2.5 years

Substituting these values into the formula:

625,000 = PV(1 + 0.06/2)^(2*2.5)

Now we need to solve for PV:

First, simplify the exponential term:
1.03^5 = 1.15927481

625,000 = PV * 1.15927481

Now, divide both sides by 1.15927481 to isolate PV:

PV = 625,000 / 1.15927481

Using a calculator, the result is approximately $539,031.08.

Therefore, Pinnacle Homes should invest around $539,031.08 now to have sufficient funds to build the homes in the future.