PV = ??
Amount = 12500
i = .12/4 = .03
n = 4(12) = 48
PV(1.03)^48 = 12500
PV = 12500/1.03^48 = 3,024.99
Amount = 12500
i = .12/4 = .03
n = 4(12) = 48
PV(1.03)^48 = 12500
PV = 12500/1.03^48 = 3,024.99
First things first, we need to calculate the future value. Using the formula for compound interest, we have:
A = P(1 + r/n)^(nt)
Where:
A = the future value ($12,500)
P = the principal amount we need to invest right now
r = the annual interest rate (12% or 0.12)
n = the number of times the interest is compounded per year (quarterly, so 4)
t = the number of years (12)
Now, let's plug in the values and solve for P:
12,500 = P(1 + 0.12/4)^(4*12)
Doing all the calculations gives us P ≈ $2,523.22.
So, if you want to have $12,500 in 12 years with a 12% interest rate, compounded quarterly, you should invest approximately $2,523.22 right now. Of course, that's assuming my calculations and comedy skills are on point!
FV = PV(1+ r/n)^(n*t)
Where:
FV = future value
PV = present value (amount to be invested now)
r = annual interest rate (as a decimal)
n = number of compounding periods per year
t = number of years
In this case, we have:
FV = $12,500
r = 12% or 0.12 (as a decimal)
n = 4 (compounded quarterly)
t = 12 years
Plugging in the values into the formula, we have:
$12,500 = PV(1 + 0.12/4)^(4*12)
Simplifying the equation further:
$12,500 = PV(1.03)^(48)
Now, divide both sides of the equation by (1.03)^48:
PV = $12,500 / (1.03)^48
Using a calculator, we find:
PV ≈ $4,186.57
Therefore, you should invest approximately $4,186.57 now at a 12% interest rate, compounded quarterly, in order to have $12,500 in 12 years.
A = P(1 + r/n)^(nt)
Where:
A = the future amount (in this case, $12,500)
P = the principal amount (the amount you should invest now)
r = the annual interest rate (12% or 0.12 as a decimal)
n = the number of times the interest is compounded per year (quarterly, so 4)
t = the number of years (12)
Plugging in the values, we can rewrite the formula as:
$12,500 = P(1 + 0.12/4)^(4*12)
Now, let's solve for P:
P = $12,500 / (1 + 0.12/4)^(4*12)
P ≈ $3,537.64
Therefore, you should invest approximately $3,537.64 now at a 12% interest rate, compounded quarterly, in order to have $12,500 after 12 years.