Effective interest rate - Haaga-Helia ammattikorkeakoulu



Effective interest rate

Example 1.

Loan = 10 000 €. Interest rate = 3,6%. Loan is paid with equal monthly payments in 2 years.

Bank charges 400 € starting fee, plus 3 € office fee for every payment.

Let’s calculate the equal payment: [pic] ; n = 2 × 12 = 24

[pic] + 3 € = 435,47 €

Cash value of the loan = 10 000 € - 400 € = 9 600 €

From customers view: Loan = 9 600 € and the equal payment = 435,47 €

The customer is interested in the real (=effective) interest rate of the loan. Obviously the rate is higher, than 3,6%. Let’s check if the effective rate is higher or lower than 6 %.

We have to calculate an equal monthly payment for 9 600 € loan with 6 % annual interest rate.

[pic] [pic] = 425,48 €

If the actual (equal) payment was 425,48 €, it would mean, that the effective rate of the loan was 6 %. Because the payment (435,47 €) is even higher, it tells us, that the effective annual rate of the loan is HIGHER than 6%.

We could go on with testing if the effective rate is higher than 7 %, 8% and so on…

[Excel: eff. rate = 8,62 %]

Example 2.

A student loans 200 € to his friend. The friend pays 5 x 45 € with 2 weeks intervals (=14 days). Lets estimate the effective annual interest rate of the loan.

Suppose the effective annual rate = i

If we discount all five payments back in to the moment when the loan was taken, we should match exactly to total of 200 €. We can write an equation for solving i:

(Note, the simple interest method is applied)

PV = [pic]

We could test the equation with i = 10% = 0,1: PV = 222,45 € (> 200 €)

Because the present value is greater than 200 € we did not discount strongly enough, which tells us that 10% is not high rate enough.

We can make few more tries:

|rate (i) |Present value |

|20 % |219,96 € |

|50 % |212,90 € |

|100 % |202,26 € |

|110 % |200,28 € |

Now we can tell, that the effective annual rate of the loan is very close to 110 %.

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