Harleen has deposited$$ $$125$ at the end of each month for $13$ years at$4\mathrm{.}68\%$ compounded monthly. After her last deposit she converted the balance into an ordinary annuity paying$$ $$890$ every three months for nine years. What is the nominal annual rate of$$ interest, compounded$$ quarterly, paid by the$$ annuity? Round the final answer to six decimal places as needed. Round all intermediate values to six decimal places as$$ needed