A collection agency pays a doctor $\$5,000$ for invoices that the doctor hasn't been able to collect on. After two years, the collection agency has collected $\$6,000$ on the invoices. At what nominal rate of discount compounded monthly did the agency receive on this transaction?
I'm trying to use the following relationship: $$a(t) = (1 + i^m/m)^{mt}$$
using the following values
$$6000 = (1 + i^{12}/12)^{12\times 2}$$
when I solved for $i^{12}$ I got the following $$ (6000^{1/24}-1)\times 12 = i^{12}$$
However this can't be the correct answer. Any help would be appreciated.