If you put S dollars in the bank each month then in n months it will have increased to . Of course, each month you will have one less month for the money added that year to accrue interest. That is the money put in the bank the first year will earn , the money put in the second month will have earned . That means that if you have a total of n months to save, and put S dollars in the account each month, at the end of those n months you will have . That is a "geometric" series, of the form with A= S and r= 1.0025. It is easy to show that the sum of such a geometric series is . For your sum that is . Put in the number of months you will have to save for each one, set it equal to 5642, and solve for S. For given n, is a specific number and solving for S means just dividing 5642 by that number.