Use the following information for questions $1$ to $2.$ Show all your calculations.

Mr$.$ Lai bought an apartment four years ago. The purchase price was $$6,000,000.$ He borrowed $60\%$ of the purchase price through a mortgage from his bank. The interest rate of the mortgage was $5\%$ p$.$a$.$ The mortgage was to be repaid monthly for $18$ years. He was not allowed to make early repayment of the principal in the first four years. After the first four years he is allowed to make any early repayment as he likes. The bank manager told Mr$.$ Lai that the mortgage interest rate has been revised to $4\%$ p$.$a$.$ starting today.

Calculate the total amount of interest Mr$.$ Lai has paid in the fourth year.

Since Mr$.$ Lai has an option to make early repayment of the principal to the bank now, he decides to make an early repayment of $$200,000$ principal today.

A$.$ After repaying the $$200,000$ today, in how many more months will the mortgage be paid off if he wants to keep the original repayment amount?

B$.$ After repaying the $$200,000$ today, what is his new monthly payment if he wants to keep the original repayment period?

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