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.

(Do you see why?)

Solve the differential equation above for the continuous annuity y(t) with deposit rate d = $7000 and continuous interest rate

r = 0.02,

subject to the initial condition

y(0) = 0

(zero initial value).

y =