# Math

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The management of Gibraltar Brokerage Services anticipates a capital expenditure of \$27,000 in 3 yr for the purpose of purchasing new computers and has decided to set up a sinking fund to finance this purchase. If the fund earns interest at the rate of 9%/year compounded quarterly, determine the size of each (equal) quarterly installment that should be deposited in the fund.

• Math -

27,000 in 3yr, 9%/yr compounded quarterly

R = Ai/(1 + i)^n - 1
R = Payment
A = Total needed = 27,000
n = Number of payments = 4 * 3 = 12
i = Interest rate = 0.09/4 = 0.0225

R = 27000(0.0225)/((1 + 0.0225)^12 - 1)
R = 607.50/((1.0225)^12 - 1)
R = 607.50/(1.30605 - 1)
R = 607.50/0.30605
R = 1984.97

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