Question

4) (5 pts) After an unfortunate series of events, you find yourself in possession of a new car – and the associated loan. Due to the particular nature of your poor decisions, you are unable to recall the interest rate. When explaining to your parents/spouse/SO/reflection, you feel that knowing the interest rate would be helpful. You know the payments are $600/month for five years, and the sticker price was $25,000. You know the formula for annual payment A is:

A=P∗ i(i+1)^n / (1+i)^(n) −1

where P is the principal, i is the interest rate (in decimal, not percentage, so 10% is entered as 0.1), and n is the number of years.

You decide, being an engineer, that you can figure this out, but algebra is letting you down. This problem will ask you to find the interest rate at various resolutions using incremental search (a terrible plan, but very easy to program).

a) Write a general-purpose incremental search function. This function should calculate the “x” (in this case, “i”) values of interest using equal spacing (the bounds, and the number of points, should be inputs to the function). Your search function should also take a function handle as an input. This function handle should be used to calculate the function value (A) at each point in the incremental search (do not merely pass in a series of i and A values, for example).

An acceptable prototype would be: function [rootLocations, numRoots] = IncSearch(func, lowerBound, upperBound, numPoints)

Decide for yourself how you wish to define numPoints (points between the boundaries or total points), but make sure you comment it appropriately.

b) Using your new function from part a, search for the interest rate using a starting bracket of 1% to 30%. Report the answer using resolution (inner interval length) of 1, 0.1, and 0.01 percentage points (you'll have to calculate the number of points required, and then call your function). Note I said resolution not e.g. ARE – I'm referring here to the distance between adjacent evaluation points on the “interest rate” axis. You'll also need to create an anonymous function using the above equation.

c) Using MATLAB's tic and toc commands (in a script file, not the command window), compare the computational complexity (time to complete) of solving this problem with each of the resolutions in part b.

Answer 1