Ramu buys a piece of land for RM$34,460\mathrm{.}16.$ He makes a down payment of RM$10,000$ and the balance is financed

through a bank. He has to pay RM$400$ a month to settle the loan.

$($a$)$ If the bank charged $12\%$ compounded monthly, determine the number of payments that will settle the loan.

$($b$)$ After paying the first $47$ monthly payments, Ramu settled the loan by making a final payment on the forty$-$

eighth payment. Find the value of this payment. What is the total interest that he has to pay?

$[$Modified exam question$]$