Takalani is now $20$ years old. Takalani's monthly salary after tax is $R45,000$ per month. Takalani would like to save R$5,000$ every month for the next $20$ years. He knows he can earn $12\%$ per annum compounded monthly on any investments he makes. Takalani's monthly expenses are R$30,000$ every month. Assume inflation to be $6\%$ every year. Assume inflation impacts only on an annual basis and therefore ignore any compounding effect.

Takalani would like to purchase a $3$ bedroom home, which is currently worth R$1,5$ million. He intends taking a home loan from his local bank which will result in him qualifying for interest rate at prime less $1\%.$ Assume prime to be $10\%.$ Also assume the bank compounds interest on a monthly basis. He wants his home loan term to be $20$ years.

Takalani has $1$ child who will be ready to enter university in $5$ years' time. The total fees including accommodation is currently R$300,000.$ It is expected that university fees escalate by $3\%$ every year. Assume that Takalani child will enrol in a $4$ year degree program.

You are required to:

a$)$ Determine whether Takalani can afford to buy his new home which is worth R$1,5$ million