a$)$ How many Canadian government bonds was able to buy with his jackpot on August $15,2018?$

b$)$ How much will Denis have accumulated by the time of retirement if he decides to go with option $1?$

c$)$ How much

will Denis have accumulated by the time of retirement if he decides to go with it$?$ option $2?$

d$)$ How much will Denis have accumulated at the time of retirement if he decides to go with option $3?$

e $)$

hwhat is the option that willmaximize Denis's pension fund on August $15,2029?$

Question $4$ : Obligations

On August $15,2018,$ your uncle Denis won the jackpot of $1\mathrm{.}5$milion$ in the "The Rooster with the Golden Legs" draw, Being very conservative and not trusting anyone since the last financial crisis, your uncle asked you for your opinion on how to invest that money without too much risk. and you suggested that he put his money into the following government bonds:

$\backslash$table$[[$Type$,$Issuer,Prize,Coupon$(\%),$Deadline,RAE$(\%)],[$Gov$,$CANADA,,$5,750,15-$Fev$-2046,3,55]]$

In today's newspapers $($February $15,2024),$ the coupons have just been paid $($and Denis has

already spent them to buy a new chair. Denis has always spent all the coupons received$)$ and we can find the following rating for this same obligation:

$\backslash$table$[[$Type$,$Issuer,Prize,Coupon$(\%),$Deadline,RAE$(\%)],[$Gov$,$CANADA,,$5,750,15-$Fev$-2046,4,78]]$

At the end of last week, at your father's party, your uncle would tell you how happy he was with the choice he had made, but he was thinking about various possibilities. Denis wants to have your opinion on his different options. He wants to use that money $($and the coupons$)$ as a pension fund, and he expects to retire in just over five years, on August $15,2029.$ Denis considers the following choices:

Keep his current bonds and sell them only when he retires, $($the yield at maturity is expected to be $5\mathrm{.}55\%$ on August $15,2029$ when he retires$),$

Sell your bonds immediately $($it$\text{'}$s February $15,2024)$ and put all that money in a balanced special fund that should yield on average a $7\%$ monthly capitalized rate until you retire.

Sell your bonds immediately and buy corporate bonds from a Small company that provides electronic equipment $($Elekno$)$ that a friend told you about. It would keep them until maturity and then invest the amount received at maturity in the famous balanced special fund offering a monthly capitalised $7\%$ rate,

Elekno's bonds are listed today as follows:

$\backslash$table$[[$Type$,$Issuer,Prix,Coupon$(\%),$Deadline,RAE$(\%)],[$Corp$,$Elekno INC,,$11,875,15-$February $2029,16,286]]$

You explained to your uncle not to spend his coupons like he used to$,$ and to invest them in an account so that he could earn interest. For each of the options, knowing that all unused money at the time of purchase $($because you do not buy fractions of bonds$)$ and coupons received can be placed in a regular account yielding an annual effective rate of $3\mathrm{.}5\%$ and that the spread $($inter$-$orice margin$)$