Question $3-10$ marks

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.