The installation of a solar thermal system of course has an investment of $ $14,545.$ The same conventional installation would have cost $ $5,890.$ The energy demand is $17,200$ kWh$/$year and the solar fraction is $67\%.$ The cost of conventional energy is $$0\mathrm{.}045$ $$/$kWh the first year, with an expected increase of $6\%$ annually. Calculate the amortization period, considering an annual inflation rate of $3\mathrm{.}5\%$