Matlab

This problem gives you practice with for loops that employ vector indexing. Be sure to follow good programming standards in your script.

Engineers regularly perform economical analyses on potential purchases needed for their projects. You are part of team working on a manufacturing productivity improvement project and are planning to take out an amortized loan to pay for necessary equipment and training. As part of the purchase and cost analysis, you must determine some information about expected payments for the loan. Amortization is one common type of loan processing. The loan has fixed payments over its life, and the payments are applied to both interest accrued and the original principle. The interest is calculated on the existing principle at the end of each payment period. Early payments in an amortized loan are mostly paying accrued interest with only small amounts paying down the original principle. Over time, the size of the interest component of the total payment decreases and the size of the principle component increases. You can calculate the fixed payment amount on an amortized loan using the equation A=(1+r)n1P[r(1+r)n] Where - P is the princple amount of the loan (i.e., the amount borrowed) - n is the number of total payments for the life of the loan - r is the periodic interest rate, in decimal form, in terms of the time period between payments (e.g., percent per month when n payments are monthly payments) You want to know how much principle has been paid back after some number of payments, t. This is called the cumulative principle payment, S. For example: You have a loan with a $1000/month payment. For the first three payments, the amount you paid towards principle was $100, then $120, and then $145. Your cumulative principle payments for those months were $100, $220, and $365. A general equation to calculate the cumulative principle payment is S(t)=Ak=1t(1+r)(nk+1) You expect the project will take out a loan with a principle of $500,000, with an annual interest rate of 10%, and paid back in equal monthly installments over a period of 15 years. You must write a script that will do the following: - Uses at least 1 FOR loop. This problem does not require any structure nested inside another. Nested structures are taught in future classes of this course and are not needed here. If you choose to use them, they must be correct. - Determine a vector of the cumulative total payments that have been paid toward the loan at each month for the entire loan period. - Determine a vector of the cumulative principle payments that have been paid at each month for the entire loan period. - Create one (1) figure that displays the cumulative principle payment vector and the cumulative total payment vector on the same axes with number of months on the x-axis. - Format the plot for professional presentation. for plotting reference