Example $4$:

A sinking fund is a fund into which periodic payments are made in order to satisfy a future obligation. Suppose a machine costing $$7000$ is to be replaced at the end of eight years, at which time it will have a salvage value of $$700.$ In order to provide money at that time for a new machine costing the same amount, a sinking fund is set up$.$ The amount in the fund at the end of eight years is to be the difference between the replacement cost and the salvage value. If equal payments are placed in the fund at the end of each quarter and the fund earns $8\%$ compounded quarterly, what should each payment be$?$