this is a mathlab code the white spot on the image can be edited but the grey spots of this code cannot be changed how can i fix this code it is not meeting one of the grading criteria Annuity this matter proves to be related to the entire code meaning the problem has to be reset where everything on the white spot must be changed to make it work

$$immy starts an annuity with a principal value of R$1000000($one million Rands$)$ and plans to withdraw a fixed amount each month, starting one

month after opening the annuity account. Jimmy expects to draw R$20000($twenty thousand Rands$)$ from the annuity every month, for $15$ years

$($fifteen years$).$ Suppose the monthly interest rate is fixed at $1\mathrm{.}9\%$ and that interest is computed each month on the annuity before the

withdrawal made. The annuity is overdrawn when its value drops below zero.

Answer the following questions:

Will the value of the annuity drop to zero before the $15$ year time span ends?

For how many months will Jimmy be able to withdraw R$20000$ without overdrawing on the account?

What is the value of the annuity after the last withdrawal of R$20000,$ before the account is overdrawn?

Use the code below to help answer these questions. The function

AnnuityRecursive$($ p$,$w$,$r$,$n$)$

takes as input the principle value p$,$ the monthly withdrawal amount w$,$ the iterest rate r and the number of months n $,$ and returns a vector t of

months and a vector a of annuity values such that a$($i$)$ is the value of the anuity at time t$($ i$).$

Note: This task will require several iterations to complete and several iterations to determine the necessary values. The code provided will

generate a plot of your simulation values to help you complete the task. You can run your code on the system before submitting your soulution

for grading.

Script o$.$

$\%$ set constants

P $=1000000$; $\%$ Principal in Rands

W$=20000$; $\%$ Withdrawal in Rands

R$=0\mathrm{.}019$; $\%$ Monthly interest rate $(1\mathrm{.}9\%)$

N $=180$; $\%$ Number of months $(15$ years$)$

$\%$ pretty print outputs

pretty$(\text{'}$Principal$\text{'},$ P$)$;

pretty$(\text{'}$Withdrawl$\text{'},$ w$)$:

pretty$(\text{'}$Rate $,$ R$)$;

pretty$(\text{'}$Months :N$)$;

$\%$ Call AnnuityRecursive to construct the t an a vectors

$[$t a$]=$ AnnuityRecursive$($P$,$ W$,$ R$,$ N$)$:

$\%$ Answer questions below:

$\%$ Will the value of the annuity drop to zero before the $20$ year time span ends?

$\%$ Yes: $1$

$\%$ No: $0$

Q$1=1$; $\%$ Q$1=1($Yes$)$ if any value is below zero, $0($No$)$ otherwise

$\%$ For how many months will Jimny be able to withdraw R$20000$ without overdrawing

$\%$ on the account?

Q$2=$ find$($a $>0,1,$ 'last'$)$: $\%$ Find the last month where the balance is positive

$\%$ What is the value of the annuity after the last withdrawal of R$20000,$ before

$\%$ the account is overdrawn?

if Q$2$ length$($a$)$

Q$3=$ a$($Q$2)$: $\%$ Value before the overdraft happens

else

Q$3=0$;

end

$\%$ This is a generic evaluation check. You cannot edit this.

$[$Q$4$t Q$4$a$]=$ AnnuityRecursive$(123456,12345,12/1000,96)$;

$\%$ Plot the results.

plot$($t$,$ a$,\text{'}$ob$\text{'})$:

xlabel$(\text{'}$time $[$months$]\text{'})$;

ylabel$(\text{'}$value $[$Rands$]\text{'})$;

title$(\text{'}$Remaining Annuity value over time. $\text{'})$;

grid;

$\%$ define functions

function $[$t a$]=$ AnnuityRecursive$($p$,$ w$,$ r$,$ n$)$

$\%$ Initialize time vector and annuity value vector

t $=1$:n$+1$; $\%$ Time vector from $0$ to n months

a $=$ zeros$(1,$n$+1)$; $\%$ Initialize annuity values to zero

a$(1)=$ pi $\%$ Initial principal value

$\%$ Loop through each month to calculate annuity values

for i $=2$:n

a$($i$)=$a$($i$-1)*(1+$ r$)-$ w; $\%$ Calculate next annuity value

if a$($i If balance goes negative, stop

a$($i$)=0$; $\%$ Set value to zero if it goes negative

break: $\%$ Exit loop

end

end

end

$\%$ Use the following functions to pretty print arrays and values

function pretty$($s$,$ a$)$

end

fprintf$([\text{'}\%$s:$\text{'}$ repmat$(\text{'}\%1$d $\text{'},1,$ numel$($a$))\text{'}$

$\text{'}],$ s$,$ a$)$:

Output