Geoff Bezos wishes to establish a perpetual scholarship fund for coders at Amazon Web Services. The first annual scholarship will be paid in four years. The amount of the scholarship will initially be $$60,000$ but will then increase by $3\%$ p$.$a$.$ in line with expected inflation. How much is required to establish the fund if it is invested at $5\mathrm{.}75\%$ p$.$a$.?$