Write two m$-$file functions that will allow you to compare mortgage calculations for the monthly

payment and compare mortgages with different loan values.

The monthly payment $M,$ is calculated using:

$M=\frac{P*(\frac{r}{12})}{1-(1+\frac{r}{12}{)}^{-12y}}$

Where $P$ is the principal loan amount, $r$ is the interest rate $($in decimal form not percent form$),$ and $y$ Is the number of years of the loan.

a$.$ Create an m$-$file function called "mortgage$\_$a$.$m$"$ that will serve as a loan calculator $($like the

ones you might find online$).$ This function will have three inputs and two outputs. The three

inputs in order are mortgage amount $($in Dollars$),$ interest rate $($in $\%),$ and years to pay off the

loan $($in years$).$ The outputs will be in the order returned: monthly payment and total of all

payments. If the Term is not input, it is assumed to be $30$ years. An example output of the

function is shown in Figure $2.$ Note: Your function will be checked with other input values whe graded.

$>[mp,tp]=$ mortgage $a(200000,7\mathrm{.}5,30)$

$mp=$

$1398\mathrm{.}43$

$tp=$

$503434\mathrm{.}45$

Figure $2$: Loan Calculator Script Input and Output

b$.$ Create a second $m-$file function called "mor ryage$\_$b$.$m$"$ that will allow you to compare

different loan amounts. This function will have two inputs and no outputs. The two inputs in

order are: the maximum mortgage amount $($in Dollars$),$ and interest rate $($in $\%).$ You can modif your file from part a for this script. Although the function does not return any values, it will

output a Table in the Command Window. Your script needs to create a loan amount vector with

a range of loan amounts $($principal$)$ from the maximum mortgage amount down to $$50,000$ less in principal in $$5,000$ increments. Calculate the monthly payments for both $15$ and $30$ year

payback plans based on the varying initial amounts for the principal. An example of the

truncated output is shown in Figure $3$ for a maximum mortgage amount of $$200000$ and an

interest rate of $7\%.($This is example output and your function should give correct values for

other inputs.$)$

Figure $3$: Loan Calculator Table Script Input and Output Format

Note: The output should continue subtracting $$5000$ from the principal on each new row until it

has subtracted $$50000$ from the cost of the house. The $.$ decimals on principals and payments should all line up for principals up to $$99,999,999.$ Your function should still have all the dollar signs in the Table aligned for larger or smaller loan amounts.