Effective Annual Rate of Interest

If the interest is 2.1% every 3 months, then the annual rate is 1.021^4 - 1 = 0.0867

Hi I am struggling with understanding the same question. Why are different formulas used to calculate effective interest rate in other questions? In some questions treatment is as below: If the nominal interest rate was 10% per year compounded on a monthly basis then the formula used is r=(1+i/n)^n -1 r =((1+0.1/12)^12 )-1 =0.1047 ×100= 10.47% So why in above question we are using (1+r)^n -1 I am obviously missing something that sets these 2 examples apart to grant different treatment. Any help will be much appreciated.

And below is an answer from the other tutors here on this website for the same question as but giving a different answer to you. " Ken Garrett Keymaster Topics: 10 Replies: 9641 ????? It’s an error and it should be: (1 + 0.021/4)^4 – 1 = 0.021166 " I am so confused. Kindly help Thankyou

The implication is the original question is that the interest rate is 2.1% every three months - not that it is 2.1% per year. We know this because it says that the 2.1% is compounded every three months (and does not say that it is 2.1% per year). If the interest rate had been given as being 2.1% per year then we would have divided by 4. If Ken had written somewhere as you have typed, then he must have misread the question.

Thankyou for your reply. I appreciate you explaining it to me but I am still confused because in many questions available in book when interest rate is compounded monthly then the interest rate is divided by 12 , but when compounded every 3 months thes interest rate is not divided by 4. Hence the confusion as to why 2 separate treatment is shown in the book. For example: In the book its is given as an illustration that: If the nominal interest rate was 10% per year compounded on a monthly basis then the formula used is r=(1+i/n)^n -1 r =((1+0.1/12)^12 )-1 =0.1047 ×100= 10.47% As above we are compounding every 12 months so why use a different formula when compounding quarterly? Again I apologise that i am unable to understand whats the difference. Thanks in advance.

It is not a question of there being a different formula. When the interest is compounded quarterly then we need the interest rate charged each quarter. If the question gives the interest each quester then you use it. If the question gives the interest rate per year, then we divide by 4 to get the interest rate charged each quarter (and this is the case in the first question). When the interest rate is compounded monthly then we need the interest rate charged each month. If the question gives the interest rate per month then you use it (and that is the case in the second question). If the question had given the interest rate per year then we would divide by 12 to get the interest rate charged each month. Do watch my free lectures on interest because the examiner is keen to test that you understand what is happening and are not just learning formulas.

Oh I finally got it. Thankyou for such a detailed and well written explanation. I appreciate your help very much. I will look into your lectures aswell. Thanks again

You are welcome :-)