Real annual interest rate

The real annual interest rate - calculated taking into account the nominal interest rate and all costs (commission, insurance and so on.).

 

Mathematical methods of calculating the real annual interest rate

                                                       formula fifd

S — net amount of loan, difference between the total amount of the loan and all current expenditures;

k — serial number of cash flows (payments);

n — number of cash flows (payments);

x — the real annual interest rate;.

m — nnual payment interval;

Ak — Sum of cash flows in k according to loan agreement. Cash outflows are added with negative sign, cash inflows are added with positive sign.

 

Example 1

According to the loan agreement, 274.11 AZN payment is made per month by borrower for 6000 AZN loan, during 24 months with 9% nominal interest rate. 60 AZN commission has been paid.

In this case, equation:

formula2 fifd

 

After calculation Real annual interest rate (IRR): x = 10.002769% ≈ 10,0%.

 

Example 2

According to the loan agreement, 274.11 AZN payment is made per month by borrower for 6000 AZN loan, during 24 months with 9% nominal interest rate. 60 AZN commission AND 10 AZN insurance cost have been paid.

In this case, equation:

formula3 fifd

After calculation Real annual interest rate (IRR): X = 10.171285% ≈ 10.2%

This means that, although the amount of issued is 6000 AZN, taking into account commissions and insurance cost, the customer receives 5930 AZN. Real annual interest rate (IRR) indicates the nominal interest rate is calculated on the amount of 5930.

Real annual interest rate (IRR) is the nominal interest rate of the loan after deduction of all costs.

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