Part of the income that a machine generates is put into a si

Part of the income that a machine generates is put into a sinking fund to pay for replacement of the machine when it wears out. If $3,000 is deposited every year at 6% interest compounded annually, how many years must the machine be kept before a new machine costing $35,000 can be purchased?

Solution

Suppose you opened an account at a bank which was paying an annual interest rate of 6% (a fraction, equivalent to 100i%). You make a deposit of 3000 at the end of each year.The interest is compounded once per period. Then the value P of the account at the end of n years is given by

This can, of course, be solved for M or n algebraically:

n = (1/1) log (1+{0.06*3000)/35000}/log (1+0.06)