please do not solve in excel and instead do by hand and show each step.

12. A loan of $5,000 can be repaid by payments of $117.38 at the end of each month for n years (that is, 12n payments), starting one month after the loan is made. At the same rate of interest, 12n monthly payments of $113.40 each accumulate to $10,000 one month after the final payment. Find the equivalent effective annual rate of interest