This is a mathlab code Jimmy 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. this is the response i am getting Variable Q$4$t has an incorrect value. this is my code $\%$ set constants

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

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

R $=0\mathrm{.}019$; $\%$ Monthly interest rate

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

$\%$ pretty print outputs

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

pretty$(\text{'}$Withdrawl$\text{'},$ W$)$;

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

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

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

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

$\%$ Answer questions below:

$\%$ Call AnnuityRecursive function

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

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

$\%$ Yes: $1$

$\%$ No: $0$

$\%$ Will the value drop to zero before $15$ years?

Q$1=$ double$($any$($a $<mtext></mtext><mn>0</mn><mi>)</mi><mi>)</mi>$; $\%$ Q$1=1($Yes$)$ if any value is below zero, $0($No$)$ otherwise

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

$\%$ on the account?

Q$2=$ find$($a $>0,1,$ 'last'$)$;

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

$\%$ the account is overdrawn?

$\%$ Value of the annuity after the last withdrawal before overdrawing

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

Q$3=$ a$($Q$2)$;

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$)$

t $=0$:n; $\%$ Time vector

a $=$ zeros$($size$($t$))$; $\%$ Initialize annuity value vector

a$(1)=$ p; $\%$ Initial principal value

for i $=2$:n$+1$

a$($i$)=$ a$($i$-1)*(1+$ r$)-$w;

if a$($i$)<mtext></mtext><mn>0</mn>$

a$($i$)>=0$

break;

end

end

end

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

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

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

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

endWill 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$20000($the

next attempt will overdraw on the account$)?$

Correctly written 'AnnuityRecursive' Function t

Variable Q$4$t has an incorrect value.

Feedback is shown for the initial error only, as subsequent failures may be due to the first error