Your aunt has $$270,000$ invested at $5\mathrm{.}5\%,$ and she now wants to retire. She wants to withdraw $$45,000$ at the beginning of each year, beginning immediately. She also wants to have $$50,000$ left to give you when she ceases to withdraw funds from the account. For how many years can she make the $$45,000$ withdrawals and still have $$50,000$ left in the end?

a$.4\mathrm{.}89$ years

b$.5\mathrm{.}89$ years

c$.5\mathrm{.}97$ years

d$.7\mathrm{.}01$ years

e$.6\mathrm{.}30$ years