After graduating from NTU at the age of $25$ years old, Vincent starts planning to establish his retirement account $($RA$)$ for CPF life plan. According to CPF board, the current CPF contribution rates of employee and employer are $20\%$ and $17\%,$ respectively.

There are three options of RA when Vincent turns $55$ years old, namely Basic Retirement Sum $($BRS$),$ Full Retirement Sum $($FRS$)$ and Escalating Retirement Sum $($ERS$),$ which are estimated at $$225,000,$ $$450,000$ and $$670,000,$ respectively, after $30-$year.

Assume the CPF$\text{'}$s contribution rates remain unchanged and the CPF pays an average $3\mathrm{.}5\%$ p$.$a$.$ interest rate for all accounts till Vincent reaches $55$ years old. Of total $37\%$ contribution rate, $10\%$ is reserved for Medisave account, which cannot be use for RA$,$ and the rest will be transferred into RA at $55$ years old. Ignore salary increment, inflation, tax and CPF housing loan.

a$.$ How much is the expected monthly salary Vincent should earn from $25$ years old at least to achieve the requirements for BRS$,$ FRS and ERS at $55$ years old?

$(7$ marks$)$

b$.$ Vincent plans to study a $2-$year full$-$time MBA at Nanyang Business School after working $5$ years in the company. How much more Vincent should earn every month to meet the three CPF Life options of RA$?$

$(8$ marks$)$

c$.$ Vincent would like to choose FRS option for his RA when he turns $55$ years old. RA will be then invested in CPF Life for $10$ years compounding at an estimated rate of return of $3\mathrm{.}5\%$ p$.$a$.$ After that Vincent can enjoy a fixed monthly payout from $65$ to $85$ years old in the post$-$retirement period. Compute the expected monthly payout Vincent will receive from CPF Life from $65$ years old onwards.

$(5$ marks$)$