Question

What is the annual effective interest rate on an investment that has earnings including payback of the original investment over 18 months paid at the end of the month listed shown in the table below given the investment required $12,000 to acquire on January 1 of the first year?

Year	1	1	1	2	2	2	2	2	2
Month	February	April	October	December	January	March	April	May	June
Earnings	1200	1500	1500	1600	600	1700	2500	1900	2000

Answer 1

[(1+Nominal monthly interest rate)12-1 When compounded monthly, Effective Annual Rate (EAR) Here, nominal monthly interest rate for an uneven monthly cash flows stream can be calculated using EXCEL FUNCTION IRR() but considering initial investment required as cash outflow at the beginning as below: December January Month February 1,200 April October March April 2,500 January May June 2,000 Earnings -12,000 1,500 1,500 1,600 600 1,700 1,900 Nominal monthly interest rate Number of months in a year 3.6162% [Calculated using IRR() function in EXCEL as per screenshot copied below] 12 Annual effective interest rate (EAR) {[(1 +3.6162%)12] -1} 53.16% EXCEL SCREENSHOT R C E G K December January 1 Month February April October March April May January June 2 Earnings -12,000 1,200 1,500 1,600 600 1,700 2,500 1,900 2,000 1,500 3 4 Nominal monthly interest rate IRR(B2:K2) [Calculated using IRR() function in EXCEL as per screenshot copied below] 5 Number of months in a year 12 (1+B4)^B5}-1 |{[(1+3.6162%)*"] - 1} 6 Annual effective interest rate (EAR)