Effective Interest Rate

Hello sir !

First of all, I want to appreciate you for you excellent way to teach the student and interested learner. You did a great website and I am one of you regular visitor. I am Bangladeshi student in Cyprus doing MBA program. I am doing my thesis on "Micro-finance Effects in Bangladesh" But it's difficult for me to find out the effective interest rate for the loan which Micro finance provide.

an example: If a borrower take loan which contains the following conditions:

Present value: 1000 TK
Interest rate 10% or 100 TK
Number of Payments: 44 weeks
Future value or total repaid 1100
Service charge : 2% or 20TK
What is the Effective annual interest rate?

MRA Bangladesh find out that Effective annual interest rate is 25.07% without service charge and 31.27% with service charge for above case.

Sir I am confused on this interest rate. Could you help me by solving this problem and explaining this. 

Effective interest rate is that interest rate which is different from simple interest rate and compound interest rate. It is calculated on the basis of nominal annual rate and number of compounding periods.

Its formula is

EIR = (1 + periodic interest rate) and its power number of periods in one year -1

Or

Effective Interest Rate = ( 1 + Annual nominal interest rate / Number of payments period )^ Number of payments period - 1

In your case, you can put above values in this formula

EIR = ( 1 + 10%/ 44) ^ 44 - 1

But if service charges are given, then effective interest rate will also increase.

We can write its formula

Effective Interest Rate = ( 1 + (Annual Nominal Interest Rate + Service charges Rate) / No. of payment period) ^ No. of payment period - 1

In your case,

EIR =  { [ 1 + ( 10% +2%)/44] ^ 44} - 1

Now, you can calculate answer by using of log.