A company will need 55,000 for a new addition. To meet this goal the company deposits money in an account today that pays 5% interest annual compound quarterly. to meet this goal in five years what would the company need to deposit today?
5 years = 20 quarters at .05/4 = .0125 per quarter
1.0125^20 = 1.282037232
so
55,000/1.282037232 = $ 42,900.47
To calculate how much the company needs to deposit today to meet the goal in five years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment (the goal amount, $55,000)
P = the principal amount (the amount needed to be deposited today)
r = the annual interest rate (5% or 0.05)
n = the number of times that interest is compounded in a year (quarterly compound means n = 4)
t = the number of years (5)
Now, let's plug in the values we know:
55,000 = P(1 + 0.05/4)^(4*5)
First, simplify the equation inside the parentheses:
55,000 = P(1.0125)^(20)
Next, multiply the exponent:
55,000 = P(1.34985880758)
Now, divide both sides of the equation by (1.34985880758) to solve for P:
P = 55,000 / 1.34985880758
P ≈ $40,745.94
Therefore, the company would need to deposit approximately $40,745.94 today to meet the goal of $55,000 in five years, given an interest rate of 5% compounded quarterly.