as Module 1: Functions and Inverses Authentic Assessment: Computing an Amortized Mortgage Payment (2 pages) The formula for computing the amortized mortgage payment for a home loan is: I (1 + 1)N M = P (1 + 1 )N - Where: M - Monthly Payment P = Mortgage Principal I = Monthly Interest N = Number of Months There are three parts to this assignment. Make sure that you show all of your work to receive full credit for your answers. This could come in handy when you decide to buy a house of your own. To reduce rounding error, round to the eighth decimal place. Part I (5 points) Find the inverse of the formula above assuming that / and A are the constants, 0.00416667 (5% rate divided by 12) and 360 (30 years) respectively. NOTE: To make the notation less confusing, you can switch to f(x) or y for M, and x for P. When you find the inverse, f- (x) represents P, and x represents M.Part II (5 points) Verify that the inverse you found in Part I and the original formula are, in fact, inverses. Again, assume that / and A are the constants. (You may want to change the notation here, as was suggested for Part I, so you are not dealing with M and P.) Part III (5 points) Using the formula in Part I, find what the principal is for a mortgage with a monthly payment of $1945.43. Round your answer to the nearest hundredth