Aura deposits $$10\mathrm{.}00$ in a bank and fifteen years later deposits $$20\mathrm{.}00.$ The interest is credited at a nominal discount rate compounded quarterly for the first $10$ years, and at a nominal interest rate of $6\%$ compounded semi$-$annually thereafter. The accumulated amount in the bank at the end of $30$ years is $$100\mathrm{.}00.$ Calculate $\text{'}$d$\text{'}.$