Suppose you take a loan of P dollars and plan to pay it back in monthly payments over Y years with an annual interest rate of p%. Letting r = p/100 (for example, if p-8, then r =0.08), your monthly payments as a function of r will be m(r)-P 2 -12Y 1. Assume your loan amount is P- $20,000 and you pay it back over Y-10 years. Graph the monthly payment function m(r) for Osr s 0.2. How do the monthly payments change as r increases? With p = $20,000 and Y-10, suppose you can afford monthly payments of at most $225. Using the graph of Step 1, estimate the maximum interest rate that you can afford. 2. 3. Assume your loan amount is P- $20,000 and you pay it back over Y-5 years. Graph the monthly payment function m(r) for 0sr s 0.2 How do the monthly payments for Y-5 and Y - 10 compare for the same values of r? Explain Make graphs of the monthly payment function with P- $20,000 and Y-5, 10, and 20 years Describe how the monthly payments vary with Y for a fixed interest rate. Explain this behavior. By graphing the monthly payment function for various values of P and Y, complete the following sentence: For the same interest rate and monthly payments, one could borrow $20,000 and pay it back over 10 years or borrow S 4. 5. and pay it back over 15 years