# math

If \$86,000 is invested in an annuity that earns 5.2%, compounded quarterly, what payments will it provide at the end of each quarter for the next 3½ years?

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1. Principal, P = \$86000
Compounding period : quarterly
interest, i = 5.2%/4 = 1.3% = 0.013
Number of periods, n = 3.5*4 = 14
R = payment per quarter

P = R(1-(1+i)^(-n))/i, or

R = Pi/(1-(1+i)^(-n))
=\$86000*0.013/(1-1/(1.013)^14)
=\$86000*(0.0785876)
=\$6758.54

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2. This answer makes no sense. the "1-1" part of the fraction would make this DNE. You cannot divide by zero.

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3. This is how the equation should look:

86,000[0.013/([1-(1+.013)^(-14)])]

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