How long will it take $$400$ to double if it earns the following rates? Compounding occurs once a year. Round your answers to two decimal places.

$7\%.$Find the present values of these ordinary annuities. Discounting occurs once a year. Do not round intermediate calculations. Round your answers to the nearest cent.

$$900$ per year for $12$ years at $16\%.$

$

$$450$ per year for $6$ years at $8\%.$

$

$$700$ per year for $6$ years at $0\%.$

$

$4200\mathrm{.}00$

Rework previous parts assuming they are annuities due.

Present value of $$900$ per year for $12$ years at $16\%$: $

Present value of $$450$ per year for $6$ years at $8\%$: $

Present value of $$700$ per year for $6$ years at $0\%$: $

$4200\mathrm{.}00$

year$($s$)$

$15\%.$

year$($s$)$

$21\%.$

year$($s$)$

$100\%.$

year$($s$)$