A company will need $35000 in 6 years for a new addition. To meet this goal the company deposits money in an account today that pays 4% annual interest compounded quarterly. Find the amount that should be invested to total $35000 in 6 years. The company should invest $□?
P(1+.04/4)^(4*6) = 35000
Now just solve for P.
To find out the amount that should be invested today to reach a future value of $35,000 in 6 years with an interest rate of 4% compounded quarterly, we need to use the future value formula for compound interest.
The formula for future value (FV) with compound interest is:
FV = P(1 + r/n)^(n*t)
Where:
- FV is the future value
- P is the principal amount (the amount to be invested today)
- r is the annual interest rate (expressed as a decimal)
- n is the number of times the interest is compounded per year
- t is the number of years
In this case, we know that FV is $35,000, r is 4% (or 0.04 as a decimal), n is 4 (quarterly compounded), and t is 6.
We can substitute these values into the formula and solve for P:
$35,000 = P(1 + 0.04/4)^(4*6)
Simplifying the formula:
$35,000 = P(1 + 0.01)^(24)
$35,000 = P(1.01)^24
Now, divide both sides of the equation by (1.01)^24 to solve for P:
P = $35,000 / (1.01)^24
Using a calculator, we find:
P ≈ $26,374.01
Therefore, the company should invest approximately $26,374.01 today in order to have $35,000 after 6 years with 4% annual interest compounded quarterly.