City wide delivery service uses vans costing $24800 each. How much will the company have to invest today to accumulate enough money to buy six new vans at the end of 4 years? City wides bank is currently paying 12% interest compounded quarterly
12% interest????
What year was this question written????
cost of 6 vans at the end of 4 yrs
= 148800
i = .03
n = 4(4) = 16
P(1.03)^16 = 148800
solve for P
To calculate the amount of money the company needs to invest today to accumulate enough money for buying six new vans at the end of 4 years, we can use the formula for the future value of an investment.
The formula for future value with compound interest is:
FV = P * (1 + r/n)^(n*t)
Where:
FV is the future value (amount needed to buy six new vans)
P is the principal amount (initial investment)
r is the annual interest rate (12% or 0.12)
n is the number of times interest is compounded per year (quarterly, so 4)
t is the time in years (4 years)
We need to solve for P, so let's rearrange the formula:
P = FV / (1 + r/n)^(n*t)
First, let's calculate the future value (FV) needed to purchase six new vans. Each van costs $24,800, so the total cost would be 6 * $24,800 = $148,800.
Next, substitute the known values into the formula:
P = $148,800 / (1 + 0.12/4)^(4*4)
Now, calculate the denominator first:
(1 + 0.12/4)^(4*4) = (1 + 0.03)^16 = 1.03^16 ≈ 1.64986
Finally, divide the future value by the denominator to get the initial investment:
P = $148,800 / 1.64986 ≈ $90,087.71
Therefore, the company needs to invest approximately $90,087.71 today to accumulate enough money to buy six new vans at the end of 4 years.