$1.$ Juan heard that she could triple her money in $24$ years if she invested it in a large telecommunications business. What nominal interest rate compounded monthly does the business offer?

$2.$You currently have $$28,000$ in your savings account. At what nominal interest rate compounded monthly would your savings grow to $$36,278\mathrm{.}66$ in $16$ years?

$3.$Katherine wants to double her money in $9$ years in an investment fund. What quarterly compounding interest rate do you suggest that she looks for?

$4.$Juan wants to double her money in $17$ years in an investment fund. What nominal monthly compounding interest rate do you suggest that she look for? $($Hint: If money doubles, the ratio of FV to PV is $2.)$

$5.$A bank charges Iron Inc. an interest rate of $4\mathrm{.}5\%$ compounded quarterly on its line of credit. If $0\mathrm{.}75\%$ was added to the effective interest rate, calculate the new interest rate compounded quarterly.

$6.$A bank has decided to set its interest rates to compound monthly on all deposits in order to give customers the same benefits as its current offering of $4\mathrm{.}25\%$ compounded quarterly. At what value should the monthly compounded interest rate be set?

$($Round to two decimal places$)$