$1.$ Say that you want to establish a scholarship fund that will make fixed payments forever. To fund the scholarship, you plan to make $10$ annual contributions of $$19$k to an investment account with an expected return of $8\mathrm{.}8\%$ interest annually. Your first contribution occurs today. If the scholarship fund makes its first payment two years following the last contribution, then what is the fixed annual payment that the scholarship fund will award? $($Round to the nearest dollar$)$

$2.$ You have an investment that earns $13\mathrm{.}4\%$ APR compounded semi$-$annually. What is the EAR? $($Express your answer as a decimal and round to the nearest ten$-$thousandth$)$

$3.$you have an investment that earns $10\mathrm{.}0\%$ APR compounded continuously. What is the EAR? $($Express your answer as a decimal and round to the nearest ten$-$thousandth$)$

$4.$ You own an investment that pays $27\mathrm{.}6\%$ EAR. What is the monthly interest rate? $($Answer as a decimal, round to the nearest ten$-$thousandth

$5.$ You own an investment that pays $9\mathrm{.}3\%$ APR. What is the monthly interest rate? $($Answer as a decimal, round to the nearest ten$-$thousandth

$6.$ What is the value of an investment that is scheduled to pay you $$23$k in $10$ years if the expected rate of return is $3\mathrm{.}05\%$ compounded quarterly? $($Round to the nearest dollar$)$

Answer all questions and show work