Stanford would like to retire in $35$ years. He recently started a new and exciting job as a marketing specialist at an international company based in Cape Town and would like to start a retirement fund. He has already saved up R$15000.$ Stanford predicts that he will need R$2000000$ each year after retirement in order to live comfortably. He expects to live $30$ years after his retirement and would also like to leave a R$4$ million inheritance for his family trust $($i$.$e$.$ at the end of the $30$ years$).$ Stanford currently earns an effective interest rate of $10\%$ per annum, which is not expected to change until he retires. Thereafter, in retirement, he will earn an interest rate of $7\%$ per annum, compounded annually.

Required:

Calculate how much money Stanford would require at his retirement date. $(4)$

Calculate the monthly payments that Stanford would need to invest in order to reach the required capital calculated in Question $2\mathrm{.}1.$