write 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. $\%$ set constants

$\%$ 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:

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

$\%$ Yes: $1$

$\%$ No: $0$

Q$1=?$

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

$\%$ on the account?

Q$2=?$

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

$\%$ the account is overdrawn?

Q$3=?$

$\%$ 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$)$

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$)$;

end