a$)$ Samy wants to retire in the next $20$ years. After his retirement, he would like to

withdraw RM$45,000$ every year for the next $20$ years until he passes away. He would

like to bequeath RM$1\mathrm{.}5$ million to his grandchildren after his death. Assuming the

interest rate from now until his retirement is $8\%$ and it decreases to $6\%$ after

retirement until he passes away, calculate how much he needs to save at the

beginning of each year until his retirement so that he is able to meet his withdrawing

objective after retirement and bequeathing when he passes away.

$(7$ marks$)$Samy wants to retire in the next $20$ years. After his retirement, he would like to withdraw RM$45,000$ every year for the next $20$ years until he passes away. He would like to bequeath RM$1\mathrm{.}5$ million to his grandchildren after his death. Assuming the interest rate from now until his retirement is $8\%$ and it decreases to $6\%$ after retirement until he passes away, calculate how much he needs to save at the beginning of each year until his retirement so that he is able to meet his withdrawing objective after retirement and bequeathing when he passes away.