A real estate development company is planning to bulid five homes, each costing $125,000, in 2.5years. the bank pays 6% interest compound semiannually. how much should the company invest now to sufficemt funds to build homes in the future?
Future value, F = 5*125000=625000
Interest, i = 6% annually = 0.06
compounding frequency, f = 2
Time, t = 2.5 years
Let
P = present value
then use the compound interest formula
F=P(1+i/f)ft
Solve for P
P=F/(1+i/f)ft
=625000/(1+0.06/2)2*2.5
=539130.49
=
To calculate the amount the company should invest now to have sufficient funds to build the homes in the future, we need to calculate the future value of the investment considering compound interest.
The formula to calculate the future value (FV) of an investment with compound interest is given by:
FV = P(1 + r/n)^(nt)
Where:
P = Principal amount (initial investment)
r = Annual interest rate (in decimal form)
n = Number of compounding periods per year
t = Number of years
In this case, the company plans to build the homes in 2.5 years and the bank pays 6% interest compounded semiannually. So, let's calculate the future value.
Principal amount (P) = ?
Annual interest rate (r) = 6% = 0.06 (decimal form)
Number of compounding periods per year (n) = 2 (semiannually)
Number of years (t) = 2.5
Using the formula, the future value (FV) can be calculated as:
FV = P(1 + r/n)^(nt)
FV = P(1 + 0.06/2)^(2*2.5)
Now, let's substitute the values and calculate:
FV = P(1 + 0.03)^5
FV = P(1.03)^5
The company needs to have a total of 5 homes, and each home costs $125,000. So, the total funds required to build the homes is:
Total funds required = Number of homes * Cost per home
Total funds required = 5 * $125,000 = $625,000
We can set up an equation to find the principal amount (P):
P(1.03)^5 = $625,000
Now, rearrange the equation and solve for P:
P = $625,000 / (1.03)^5
Using a calculator, evaluate (1.03)^5 and divide $625,000 by the result to find the principal amount (P).