An annuity is a fund into which one makes equal payments at regular intervals. If the fund earns interest at rate r compounded continuously, and deposits are made continuously at the rate of d dollars per year (a continuous annuity), then the value y(t) of the fund after t years satisfies the differential equation y'= d+ry.t (Do you see why?) Solve the differential equation for the continuous annuity y(t) with deposit rate d = $2000 and continuous interest rate r = 0.08, subject to the initial condition y(0) = 0 (zero initial value).

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