a$.$ Jane is planning to save up for a trip to Switzerland in $3$ years. She estimates that she will need $$60,000$ for this trip. Currently, Jane has $$35,000$ in a savings account paying $4\mathrm{.}1\%$ per annum, compounded quarterly. To finance this trip, she plans to use her current savings plus what she can obtain by making three equal annual investments in an ASX $200$ index fund, with the first investment starting today. The ASX $200$ index fund will pay a rate of return of $7\%$ per annum, compounded annually. How much money should Jane invest every year in the index fund to finance this trip? $(6$ marks$)$