Muthu is $40$ years old and has saved nothing for his retirement.

However, he has just inherited RM$200,000$ from his grandfather and wants to invest it in a retirement plan.

He plans to put the money in an investment account, earning an $8\%$ return.

He will let the money accumulate for $20$ years when he retires at $60.$

He would like to deposit enough money to begin making withdrawals of RM$55,000$ per year, starting at $61$ until he reaches age $80.$

He wants to balance his account after the last withdrawal to zero $($RMO$)$ once he reaches the age of $80$ years old.

Question:

A$.$ How much money does he need in the year $(0),$ i$.$e$.$ age $40,$ to achieve his retirement goal at $65?$

B$.$Suppose Muthu has changed his mind and invested the entire inheritance into the account, eaming $8\%.$ After his last withdrawal at age $80,$ he wants to leave the remaining money to his nephew.

How much would his nephew receive when Muthu withdraws the final annual instalment of RM$55,000$ at the age of $80?$