Pinnacle Homes, a real estate development company, is planning to build five homes, each costing $125,000, in 2 1/2 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?
amount(1.03)^5 = 5(125000)
I got $ 539,130.49
post it.
To determine how much Pinnacle Homes should invest now, we can use the formula for future value of an investment with compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the interest rate
n = the number of times interest is compounded per year
t = the number of years
In this case, Pinnacle Homes wants to have enough funds to build the homes in 2 1/2 years. So, t = 2.5 years, the interest rate is 6% (or 0.06), and interest is compounded semiannually, so n = 2.
Let's calculate the future value of one home:
A = $125,000(1 + 0.06/2)^(2*2.5)
= $125,000(1 + 0.03)^5
= $125,000(1.03)^5
≈ $125,000(1.159274)
≈ $144,909.25
Now, to calculate the total amount Pinnacle Homes should invest, multiply the future value of one home by the number of homes they want to build:
Total investment = $144,909.25 * 5
= $724,546.25
Therefore, Pinnacle Homes should invest approximately $724,546.25 to have sufficient funds to build the homes in the future.