P$4.(40$ pts$.)$ A family is saving for their daughter college education, and they would like to

see if after $18$ years their savings will be enough to avoid the need for student loans. They

started the saving process with a deposit from the grandparents of $$5,000,$ and they plan on

depositing $$300$ per month for the next $18$ years. Suppose that the annual rate of return

$($APR$)$ on the savings is $3\%$ and that interest is compounded monthly $($monthly interest

earned is balance$*$APR$/12).$

The monthly balance can be calculated according to the formula:

New Balance$=$Previous Balance $+$ Monthly Interest Earned $+$ Monthly Contribution

Create a Matlab program based upon a "for" loop to determine the balance at the end of each

month for the next $18$ years. The results for each month should be placed in a vector $($in other

words, the balance at the end of each month is saved as a separate entry in the vector$).$

It is projected that tuition will increase on average $5\%$ per year, and the current in$-$state

tuition is of $$8,000$ per academic year.

The objective of the program is to determine if the amount saved by the family will be

enough to cover for $4$ years of college cost.

The program should do the following:

a$)$ It may start with defined parameters as given in the problem above, or it is preferred for

the code to start with input functions asking for all initial parameters:

Number of saving years

Initial deposit

Annual rate of return

Monthly contribution

Current annual in$-$state tuition

Rate of annual increase of the in$-$state tuition

b$)$ Calculate the balance vector with monthly data. Do not display all the data $($too many

data to display$),$ but at the end of the calculations display ONLY the value of the savings

at the end of the ${18}^{th}$ year;

c$)$ Calculate a vector with annual tuition for the next $21$ years, and determine the total

amount of tuition needed for the years $18$ through $21.$ Display the tuition amounts needed

for the years $18$ to $21$ as well as the total amount needed for the $4$ years of college.

d$)$ Compare the savings and the tuition needed and generate a statement stating if the saving

is adequate to pay the total tuition or if extra money are needed.

e$)$ Plot the monthly balance over the $216$ months $(18$ years$)$; on the same plot add a

reference horizontal line set for the value of the total tuition needed; the plot should be

fully labeled.