For this Project you will examine the financial called a Mortgage in terms of a Recurrence Relation, and use the solution to come up with an equation for a Monthly Payment. You should not have to any further research, but you may wish to familiarize yourself with the terminology. And considering the likelihood of being personally involved with a mortgage in the future, it couldnt hurt to be well informed. If you do any external research be sure to properly cite your sources. If you work with another student(s), please include their name(s) in the write-up as well. If you use any electronic resources to help you track the possible sequences or perform calculations, name them in the report, and include sample calculations (in the case of something like a spreadsheet, a very common financial tool) or sample code (in the case of a common business-oriented language"). You do not need to include the actual, executable program in the report.

A basic mortgage can be considered thusly:

Take a starting value, called the Principal. At the end of the month, add a percentage, called the Interest Rate, of the current value to itself, and then subtract a fixed amount, the Monthly Payment. Repeat until the value reaches zero.

Express the given method as a Recurrence Relation in terms of the variables P, r, and M. Then solve the relation for the value as a function of the current month. Finally, solve for M, the Monthly payment. How does M change as the Principal increases? As the Rate increases? As the Number of months in the loan increases? As the Number of months approaches infinite?

EDIT: Express the recurrence relation in terms of the variables P, r, and M for: Take a starting value, called the Principal. At the end of the month, add a percentage, called the Interest Rate, of the current value to itself, and then subtract a fixed amount, the Monthly Payment. Repeat until the value reaches zero.

The expression would be used separate times to solve the questions.