1. Consider a savings account started with an initial deposit of y(0) dollars. The interest rate is r percent per annum and the interest is compounded every month. The depositor is allowed to make additional deposits every month, say, u(1), u(2), u(3), and so on. Write a difference equation that will model the balance at the end of any month, expressing it in terms of previous balance, the amount deposited during the month, and the interest accrued during the month.
Now, use the model you developed to find the total balance after 5 years if a person starts with an initial deposit of $500 on the first day of a given month and deposits $100 on the first day of every subsequent month. The interest rate is10% per annum and is compounded on the last day of every month. Assume that the number of days in a month is equal.
First, I build the model.
Let A(n) be the balance at the end of the nth month. We have to following induction.
A(0)=y(0) is the initial deposit. The annual rate is r and thus the monthly rate is ...
Difference equations are investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.