What sinking fund payment would be required at the end of each three-month period, at
8% interest compounded quarterly, in order to amount to $20,000 within five years?
solve for x
20000 = x[1.02)^20 - 1]/.02
I got 823.13
To calculate the sinking fund payment required at the end of each three-month period, we need to use the sinking fund formula:
A = P * (1 + r/n)^(nt)
Where:
A = Future value (the desired amount of $20,000)
P = Payment amount at the end of each period (unknown)
r = Annual interest rate (8% or 0.08)
n = Number of compounding periods per year (quarterly compounding, so 4)
t = Number of years (5)
We want to solve for P in this equation.
Rearranging the formula, we get:
P = A / ( (1 + r/n)^(nt) )
Substituting the given values:
P = 20000 / ( (1 + 0.08/4)^(4*5) )
Now let's calculate the sinking fund payment required:
P = 20000 / ( (1 + 0.02)^(20) )
P = 20000 / (1.02^20)
P = 20000 / 1.485947
P ≈ $13,464.49
Therefore, the sinking fund payment required at the end of each three-month period to amount to $20,000 within five years, with 8% interest compounded quarterly, is approximately $13,464.49.