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How much will you pay to buy an asset today that will pay you $10,000 every month, with the first payment beginning nine months from now and the last payment exactly 3 years from now? The account pays 1% interest every month. Show supporting calculations.

Richard has just purchased an apartment at a price of $9 million. He made a downpayment of $4 million and financed the remaining balance with a 20-year mortgage at 6% per annum, compounded monthly.

(i) Determine the size of the fixed month-end payment

Assume the interest rate increases to 8.4% per annum, compounded monthly immediately after the 44th payment. If Richard decides to keep the number of remaining payments unchanged, calculate the size of the new monthly payment.