Question $2\mathrm{.}17$

Mr A $.$ Miller is a young financial director of a listed company. Although he enjoys his work, he wants to retire at the age of $35($in $10$ years' time$)$ and go sailing in the Mediterranean around the Greek islands. He estimates that he will need to have R$1\mathrm{.}2$m to buy the yacht and an additional R$200000$ to pay for supplies and mooring costs. Mr Miller intends to make equal annual payments into a bank account on which he can earn $6\%$ interest compounded annually.

$($a$)$ What amount must Mr Miller pay annually to achieve his objective in $10$ years' time? The first payment is to be made at the end of the first year.

$($b$)$ Instead of making equal annual payments, Mr Miller wants to make one single sum payment today, investing it at $6\%$ interest compounded annually. What should this single sum be$?$

Note : this is a financial management Question