Zhang wants to accumulate at least $$55,000$ by depositing $$1,500$ at the end of every month into a fund that earns interest at $5\mathrm{.}25\%$ compounded monthly.

a$.$ How many deposits does she need to make to reach her goal?

Round to the next payment

b$.$ How long will it take thang to reach her goal?

years months

Express the answer in years and months, rounded to the next payment period