Question $2(13$ marks$)$

Mathew wants to save money to meet three objectives:

$($a$)$ He wishes to retire $30$ years from now with retirement income of R$25000$ per month for $20$ years, with the first payment to be received $30$ years and one month from now.$-$

$($b$)$ He would like to purchase a retirement home in North Coast of KwaZulu Natal in $10$ years' time at an estimated cost of R$350000.$

$($e$)$ He anticipates passing away after $20$ years of retirement at which point, he wishes to leave an inheritance of R$750000$ to his nephew Xola.

He will earn $11\%$ interest per annum before he retires, and $9\%$ per annum compounded monthly after he retires.

Required:

Calculate the lump$-$sum investment Mr Mathew must make today, in order to be able to meet his three objectives. $(13$ marks$)$