what sinking fund payment would be required at the end of each six-month period, at 12% interest compounded semiannually, in order to amount to $40,000 within four years?
Paym(1.06^8 - 1)/.06 =40000
payment = 4000(.06)/(1.06^8 - 1)
= $ 4041.44
A sporting goods store recorded net sales of $526,200 for the year. The store's beginning inventory at retail was $232,100 and its ending inventory at retail was $215,100, what would be the inventory turnover at retail, rounded to the nearest tenth?
To calculate the sinking fund payment required to amount to $40,000 within four years at a 12% interest rate compounded semiannually, we can use the formula for calculating the future value of an ordinary annuity:
FV = P * ((1 + r)^n - 1) / r
Where:
FV = Future value (the desired amount of $40,000)
P = Periodic payment (the sinking fund payment we want to find)
r = Interest rate per period (12% per year, compounded semiannually, so the rate per period will be 12% / 2 = 6% or 0.06)
n = Number of compounding periods (in this case, 4 years * 2 compounding periods per year = 8 periods)
Plugging in the values, we have:
$40,000 = P * ((1 + 0.06)^8 - 1) / 0.06
Let's solve for P:
$40,000 * 0.06 = P * ((1 + 0.06)^8 - 1)
$2,400 = P * ((1.06)^8 - 1)
Now, let's calculate (1.06)^8:
(1.06)^8 ≈ 1.593848
Substituting back into the equation:
$2,400 = P * (1.593848 - 1)
$2,400 = P * 0.593848
Now, solve for P:
P = $2,400 / 0.593848
P ≈ $4,040.11
Therefore, a sinking fund payment of approximately $4,040.11 would be required at the end of each six-month period to amount to $40,000 within four years, considering a 12% interest rate compounded semiannually.