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# Calculating APR using Newton Raphson - excel spreadsheet

Posted on 2014-01-06
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Last Modified: 2014-01-09
I am trying to calculate APR based on UK rules. Here is a booklet with some details in

http://www.creditunion.ie/files/file_20050316024652OFT%20-%20Credit%20Charges%20and%20APR.pdf

The formula is on page 9.

Later on the booklet advises how to solve the formula (p52) using Newton Raphson and I need help doing this

The first step is to calculate ¿PV which represents the sum (total) of the PVs for the instalments minus the sum of the PVs for the advances.

I am not sure what the difference is between an installment and an advance? I am assuming an installment is a repayment. The booklet says there is normally one advance so I am presuming it is the amount borrowed. The booklet says PV is calculated according to the formula PV = Ax^t

The next step is to calculate ¿dV which represents the sum of the dVs for the instalments minus the sum of the dVs for the advances. The derivative is calculated as tAx^(t-1).

I have put all of these steps into a spreadsheet and I hope they are right. I have put in an initial guess of x as 1.001 as recommended by the booklet. However if i then take my new value of x as calculated by the spreadsheet and feed it back in (0.95) at cell B4, the answer for the apr moves further away. Please can you advise where I am going wrong in my calculations. I thought that by feeding the value for x back in manually I would be simulating solving the problem by Newton Raphson

http://www.dev3.co.uk/temp/interest_calculator.xlsx

Many thanks in advance for any help you can give.
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Question by:andieje
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4 Comments

LVL 24

Expert Comment

Can I ask why you are using the Newton method and not the IRR method?
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LVL 24

Expert Comment

File attached with IRR method.
interest-calculator.xlsx
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LVL 19

Accepted Solution

Ken Butters earned 500 total points
Attached is the update for the Newton Method.

The main error was in CELL D30

In this case you had a loan for 10,000.   The present value for the loan at time zero is always going to be 10,000.

Once that change was made, then repeatedly copying the value from Cell B33 to Cell B4 results in the correct interest rate in cell B34.

Without that change your present value of the loan kept incorrectly changing... forcing you to get further and further away from the true interest rate.
interest-calculator.xlsx
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Author Closing Comment

Thank you so much. I was so close :)
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