A company will need $30,000 in 7 years for a new addition. To meet this goal the company deposits money in an account that pays 7% anual intrest compound quarterly. Find the amount that should be invested to reach $30,000 in 7 years?
P(1 + .07/4)^28 = 30000
solve for P
To find the amount that should be invested to reach $30,000 in 7 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = final amount
P = principal amount (initial investment)
r = annual interest rate (in decimal form)
n = number of times the interest is compounded per year
t = number of years
In this case, we know:
A = $30,000
r = 7% = 0.07 (expressed as a decimal)
n = 4 (quarterly compounding)
t = 7 years
Now, let's substitute the known values into the formula and solve for P.
$30,000 = P(1 + 0.07/4)^(4*7)
Simplifying further:
$30,000 = P(1 + 0.0175)^28
Divide both sides by (1 + 0.0175)^28:
$30,000 / (1 + 0.0175)^28 = P
Using a calculator:
P ≈ $19,269.64
Therefore, the amount that should be invested to reach $30,000 in 7 years is approximately $19,269.64.