You have $20$ years left for your retirement. You wish to accumulate a

sum large enough by that time which will allow you an annual withdrawal

of $$100,000$ every year for $30$ years. The average interest rate between

now and the $20$th year is likely to be $4\%$ p$.$a$.$ From then onwards, for

the next $30$ years, it is likely to be $6\%$ p$.$a$.$

How much should you save in an interest$-$bearing account at the end of

each month to be able to have enough money at the time of retirement

which will allow you your desired withdrawal of $$100,000$ every year

for $30$ years after retirement? Assume that the interest in the

interest$-$bearing account is compounded monthly.