Consider the recurrence relation defined in Example 33 FROM

Consider the recurrence relation defined in Example 3.3 (FROM TEXT BOOK, also discussed in class and shown in slides) Suppose that, as in the example, you borrow $500, but you pay her back $100 each week. Each week, Ursula charges you 10% interest on the amount you still owe, after your $100 payment is taken into account Write down a recurrence relation for M(n), the amount owed after n weeks. How much will you owe after four weeks?

Solution

Q2-b The Amountwe borrowed was 500$

now at the end of first week we payed 100$ now we are left wift with 400$ and a 10% intrest is applied on 400%

so we are now left with a debt of 440$ after 1 week

now we pay another 100$ at the end of 2nd week now we are left with 340 $ and a 10% intrest on 340$ is again applied so the amount becomes 374$

now we pay another 100$ at the end of 3rd week now amount left is 274$ and intrest of 10% is applied the amount becomes 301.4$

now at the end of 4 weeks we pay another 100$ and then we are left with 201.4$

so after four weeks we owe 201.4$