On April $1,$ Year $2,$ Eleanor made a deposit of $$100,000$ in a fund and left the fund undisturbed for four years to earn compound interest at a rate that did not change during the four$-$year period. At the end of four years, the fund had a balance of $$132,088\mathrm{.}60.$ If interest was compounded quarterly, what was the annual rate of interest earned on the deposit?