Youre purchasing a family car, and a generous family friend offers you a $15,000 loan and you have to repay it in the next 20 years. However, the repayment plan is unique :

For the first 4 years, you pay p dollars annually. Over the next 6 years, the annual payment increases to 2p dollars. Then, for 5 years, it becomes 3p dollars. Finally, in the last 5 years, it reaches 4p dollars.

First create timelines to visualise these changing payments, and then calculate p in terms of the present value of annuities symbol (an) for each phase of the loan.