In this question you will be asked to represent a word probl

In this question, you will be asked to represent a word problem in mathematical terms. You will only have to enter your final answer into WebAssign, but you should keep hold of the paper that shows your intermediate calculations.

Suppose that you borrow 10000 dollars from a bank, and that the bank charges 5 percent annual interest, compounded monthly, on the loan. You make monthly payments of 50 dollars at the end of each month.

Write down a word equation that can be used to calculate the amount that is owed on the loan at the end of the month in terms of the amount owed at the start of the month.

Writing the monthly balance (i.e. how much is owed) as y_n , translate your word equation into mathematical terms. Simplify this equation.

If we write

y_n+1 = a y_n + b ,

what are the values of a and b?

a =   1.04 x(shows wrong)
b = 50x(shows wrong)

What is the value of y₀?

y₀ = 10,000

Solution

a = 1.0041

b = -50

y(0) = 10000

since the interest is 5 percent annually and ompounded monthly

after a month the amount y(n) will change to

y(n) * (1+0.05/12)

subtract 50 from it since we have paid it.

So

y(n+1) = y(n) * (1+0.05/12) - 50