$36.$ How much interest can be accumulated during one year on a $$1,000$ deposit paying

continuously compounded interest at an APR of $10\%?$

A$.$ $$100\mathrm{.}00$

B$.$ $$105\mathrm{.}17$

C$.$ $$110\mathrm{.}50$

D$.$ $$115\mathrm{.}70$

$37.$ How much interest will be earned in the next year on an investment paying $12\%$

compounded annually if $$100$ was just credited to the account for interest?

A$.$ $$88$

B$.$ $$100$

C$.$ $$112$

D$.$ $$200$

$38.$ A loan officer states, "Thousands of dollars can be saved by switching to a $15-$year

mortgage from a $30-$year mortgage." Calculate the difference in payments on a $30-$year

mortgage at $9\%$ interest versus a $15-$year mortgage with $8\mathrm{.}5\%$ interest. Both mortgages are for

$$100,000$ and have monthly payments. What is the difference in total dollars that will be paid

to the lender under each loan? $($Round the monthly payment amounts to $2$ decimal places.

Both interest rates are compounded monthly.$)$

A$.$ $$89,211$

B$.$ $$98,406$

C$.$ $$112,410$

D$.$ $$124,300$

please explain these with formulas

:$)$