A company will need 50,000 in 6 years to add a new addition. To meet this goal a company depsoits money in account that pays 7% annual intrest quarterly. Find the amount that should be deposit today to reach the goal of 50,000 in 6 years.
How much should the company deposit today?
plz help .
To determine the amount that should be deposited today, we can use the concept of compound interest. The compound interest formula can be written as:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial deposit)
r = the annual interest rate (in decimal form)
n = the number of times the interest is compounded per year
t = the number of years
In this case, we have:
A = $50,000
r = 7% = 0.07 (decimal form)
n = 4 (quarterly compounding)
t = 6 years
Now let's plug in these values and solve for P:
50,000 = P(1 + 0.07/4)^(4*6)
To simplify the calculations, let's first calculate inside the parentheses:
50,000 = P(1 + 0.0175)^(24)
Now, let's calculate (1 + 0.0175)^24 = 1.0175^24 ≈ 1.45382
50,000 = P * 1.45382
Dividing both sides by 1.45382, we find:
P ≈ 50,000 / 1.45382 ≈ $34,418.83
Therefore, the company should deposit approximately $34,418.83 today to reach its goal of $50,000 in 6 years.