A company will need $35,000 in 7 years for a new addition. To meet this goal, the company deposits money in an account today that pays 4% interest compounded annually. Find the amount to the nearest hundred dollars that should be invested to total $35,000 in 7 years.
x(1.04)^7 = 35000
solve for x
let me know what you get.
To find the amount that should be invested today, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment ($35,000 in this case)
P = the principal amount (the amount to be invested today)
r = the annual interest rate (4% in this case)
n = the number of times interest is compounded per year (since it is compounded annually, n = 1)
t = the number of years (7 years in this case)
Now let's plug in the values into the formula and solve for P:
35,000 = P(1 + 0.04/1)^(1*7)
Simplifying the equation:
35,000 = P(1.04)^7
Divide both sides of the equation by (1.04)^7:
35,000 / (1.04)^7 = P
Using a calculator, we evaluate (1.04)^7 to get approximately 1.31593. Now we can calculate P:
35,000 / 1.31593 ≈ P
P ≈ $26,593.90
Therefore, to the nearest hundred dollars, the company should invest approximately $26,600 in order to have $35,000 in 7 years.