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 5 years?
To determine the sinking fund payment required at the end of each three-month period, we need to use the formula for the future value of an annuity.
The formula for the future value of an annuity is:
FV = P * ((1 + r)^n - 1) / r
Where:
FV = Future Value (in this case, $20,000)
P = Payment per period (the sinking fund payment we need to find)
r = Interest rate per period (8% compounded quarterly, i.e., divided by 4 since it's quarterly)
n = Number of periods (in this case, the sinking fund payment will be made quarterly for 5 years, so 5 * 4 = 20 periods)
Now we can plug in the values into the formula and solve for P:
$20,000 = P * ((1 + 0.08/4)^20 - 1) / (0.08/4)
Simplifying the equation further:
$20,000 = P * (1.02^20 - 1) / 0.02
To solve for P, we can rearrange the equation:
P = ($20,000 * 0.02) / (1.02^20 - 1)
Calculating the value using a calculator:
P ≈ $512.75
Therefore, a sinking fund payment of approximately $512.75 would be required at the end of each three-month period, at 8% interest compounded quarterly, in order to amount to $20,000 within 5 years.