SOLUTION: Buying Equipment Harv, the owner of Harv’s Meats, knows that he must buy a new deboner machine in 4 years. The machine costs $12,000. In order to accumulate enough money to pay

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Question 366594: Buying Equipment Harv, the owner of Harv’s Meats,
knows that he must buy a new deboner machine in 4 years.
The machine costs $12,000. In order to accumulate enough
money to pay for the machine, Harv decides to deposit a
sum of money at the end of each 6 months in an account
paying 6% compounded semiannually. How much should
each payment be?
Answer by Tiger-T(2) About Me  (Show Source):
You can put this solution on YOUR website!
12000 = A(1.03)^(1/2) + A(1.03)^1 + A(1.03)^(3/2) + A(1.03)^2 + A(1.03)^(5/2) + A(1.03)^3 + A(1.03)^(7/2) + A(1.03)^4
Multiply the above equation through by (1.03)^(1/2) giving
12000(1.03)^(1/2) = A(1.03)^1 + A(1.03)^(3/2) + A(1.03)^2 + A(1.03)^(5/2) + A(1.03)^3 + A(1.03)^(7/2) + A(1.03)^4 + A(1.03)^(9/2)
Now subtract the first equation from the second to give
12000(1.03)^(1/2) - 12000 = A(1.03)^(9/2) - A(1.03)^(1/2)
12000[1.03)^(1/2) - 1] = A[1.03^(9/2) - 1.03^(1/2)]
A = 12000[1.03^(1/2) - 1] / [1.03^(9/2) - 1.03^(1/2)]
A = $1402.68