# business math

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I'm trying to solve this problem: 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. I just need to know how to work the problem correctly.

• business math -

you didn't give a time limit for the \$20,000, so I'll assume 5yrs

FV = PMT * (((1 + i)^n - 1)/i )
x = amt of PMT
i = rate
n = no. of payments

i = .08/4 quarters = .02
n = 4 * 5 yr = 20 payments

20,000 = x *((1 + .02)^20 - 1 )/.02
20,000 = x *(( 1.02 )^20 - 1)/ .02
20,000 = x *(1.48595 - 1)/.02
20,000 = x * (0.48595)/.02
20,000 = 0.48595x/.02
400 = 0.48595x
x = 823.13

PMT = x = \$823.13

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