Suppose that you and your friend both need to borrow the same amount of money.

You borrow money from Bank A$,$ which offers loans at an annual interest rate of $4\mathrm{.}7\%$ with continuous compounding.

Your friend borrows money from Bank B$,$ which offers loans an annual interest rate of $4\mathrm{.}6\%$ with monthly compounding.

If both loans have the same future value and the term of your loan is $117$ months, what is the term of your friend's loan $($in months$)?$