If 15% interest is compounded every two months

Question

Then the equivalent weekly compounded rate equals 1. 14.464% 2. 14.484% 3. 14.816% 4. 14.837% 5. None of the above

Answer 1

15% annually is 2.5% (15/6) every two months, compounded over the year gives 1.025^6-1=1.15969-1=0.15969 or 15.97%, which is 15.97/52 weekly=0.3071%. If 15% is the result of applying compound interest, then (1+r)^6=1.15, so r (the 2-monthly rate)=0.023567 or 2.3567%. If 15% is spread over 52 weeks, we have 15/52=0.28846%, then over a year we have 1.0028846^52=1.161583 or 16.15%. If 15% is the result of applying a weekly rate of 0.28846%, then (1+r)^52=1.15 so r=0.002691 or 0.2691%. Taking a month as 30.6 days, two months is 61.2 days and 61.2*0.2691=16.47% approx.