Mr$.$ Chan has donated $$1$ million to a college to set up a perpetuity for the purchase of books and journals for a new library to be built and named in his honour. The donation will be invested and earnings will compound for three years, at which time the first of the quarterly perpetuity payments will be made. If the funds earn $6\%$ compounded quarterly, what will be the size of the payments? $($Do not round intermediate calculations and round your final answer to $2$ decimal places.$)$

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