$5.$ A contract calls for payments of $544\mathrm{.}79$ every two months for several years. Each

payment is to be replaced by two payments of $271\mathrm{.}31,$ one to be made $1$ month before,

and one to be made at the time of$,$ the original payment. Find the monthly rate of

interest implied by this proposal, if the new payment scheme is financially equivalent

to the old one

Correct answer is $0\mathrm{.}8\%,$ please show solution