a company needs $55,000 in 7 years for a new addition. To meet this goal, the company needs to deposit money in an acct today that pays 5% annual interest compounded quarterly. What amount should the company invest to total $55,000 in 7 years?
Thanks!
P = Po*(1+r)^n.
P = $55,000.
r = 5%/4/100% = 0.0125.
n = 7yrs. * 4Comp./yr. = 28 Compounding
periods.
Solve for Po.
To calculate the amount the company should invest to reach a total of $55,000 in 7 years with a 5% annual interest rate compounded quarterly, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the future value (in this case, $55,000)
P is the principal amount (the initial investment we need to find)
r is the annual interest rate (5% or 0.05 in decimal form)
n is the number of times the interest is compounded per year (quarterly, so 4 times a year)
t is the number of years (7 years in this case)
Now, let's solve for P:
$55,000 = P(1 + 0.05/4)^(4*7)
First, we simplify the formula:
$55,000 = P(1.0125)^28
Next, we raise the base (1.0125) to the power of 28:
$55,000 = P * 1.4185
Now, we isolate P by dividing both sides of the equation by 1.4185:
P = $55,000 / 1.4185
Using a calculator, we find that P ≈ $38,743.09
Therefore, the company should invest approximately $38,743.09 today to reach a total of $55,000 in 7 years at a 5% annual interest rate compounded quarterly.