Nopay $Ltd,$ a local real estate developer, is selling uncompleted flats with occupation$-$permit

date $24$ months from today. All units are equally priced at $$10$ million. Nopay only offers two

payment plans as follows:

Plan A: The buyer makes the first payment of $x\%$ of the price today and pays the remaining

price at the end of the $24$th month.

Plan B: If the buyer buys with a lump$-$sum payment, a $5\%$ discount off the property price will be

given.

The market interest rate is $5\%$ per year compounded monthly. The initial deposit $x\%$ is

nearest:

a$)43\mathrm{.}20\%$

b$)45\mathrm{.}31\%$

c$)47\mathrm{.}35\%$

d$)49\mathrm{.}42\%$

e$)51\mathrm{.}71\%$