a company will need $30.000 in 7 years for a new addition. To meat this goal the company deposits money in an account today that pays 7% annual interest compounded quarterly.
find the amount that should be invested to total $30.000 in 7 years?
i = .07/4 = .0175
n = 7(4) = 28
x(1.0175)^28 = 30000
x = 30000/1.0175^28 = $ 18456.85
Post it.
To find the amount that should be invested today to total $30,000 in 7 years, we can use the formula for compound interest:
A = P (1 + r/n)^(nt)
Where:
A = the future value (in this case, $30,000)
P = the principal amount (the amount to be invested today)
r = the annual interest rate (7% in this case)
n = the number of times interest is compounded per year (quarterly compounding means n = 4)
t = the number of years (7 years in this case)
We can rearrange the formula to solve for P:
P = A / (1 + r/n)^(nt)
Plugging in the given values, we have:
A = $30,000
r = 7% or 0.07
n = 4
t = 7
P = $30,000 / (1 + 0.07/4)^(4*7)
Now we can calculate the value:
P = $30,000 / (1.0175)^(28)
P = $30,000 / 1.346856
P ≈ $22,286.60
Therefore, the company should invest approximately $22,286.60 today to meet their goal of $30,000 in 7 years, considering a 7% annual interest rate compounded quarterly.