Lily borrows 10,000. She will pay it with 36 monthly payments (at the end of each month) as follows. For the first 12 months she pays X + 100 per month. For the second 12 months she pays X per month. For the last 12 months she pays X - 100 per month. The nominal annual interest rate is i⁽¹²⁾= 12%.

Find X by doing the following:

a) Turn this into a 3-year annuity immediate by finding the accumulated value at the end of each 12-month period of those 12 payments.

b) Turn this into the sum of a level pay annuity plus an arithmetically decreasing annuity.