$513.($Solving for n$)($Related to Checkpoint $5\mathrm{.}5$ on page $175)$ How many years will the following take?a$.$ $$500$ to grow to $$1,039\mathrm{.}50$ if its invested at $5$ percent compounded annually b$.$ $$35$ to grow to $$53\mathrm{.}87$ if its invested at $9$ percent compounded annuallyc. $$100$ to grow to $$298\mathrm{.}60$ if its invested at $20$ percent compounded annually d$.$ $$53$ to grow to $$78\mathrm{.}76$ if its invested at $2$ percent compounded annually