# How to calculate interest charged on my loan given a series of dates & payments?

I want to calculate the interest rate payed for this loan using Mathematica.

The initial amount was of 12000€, then they asked to pay 240€ for opening the loan and another 870€ for the insurance for 10 years. And then starts interests which are called: Abschlußposten.

I would like calculate the interests percentage starting from how much I'm paying.

As a formula, I think the amount due to someone after a NumberOfDays is calculated as: `LoanAmount*(1 + InterestTax / 100)^(NumberOfDays/365)`. After every payment, the due amount decrease. But it's possible to use the same formula.

How can I set this kind of calculation? Are my supposition correct?

``````Rückzahlung 10/01/2014  171 eur
Abschlußposten  09/30/2014  -308 eur
Rückzahlung 09/29/2014  350 eur
Rückzahlung 09/25/2014  150 eur
Rückzahlung 09/23/2014  50 eur
Rückzahlung 09/01/2014  171 eur
Rückzahlung 08/01/2014  173 eur
Entgelt 07/30/2014  -1 eur
Rückzahlung 07/01/2014  173 eur
Abschlußposten  06/30/2014  -315 eur
Rückzahlung 06/02/2014  173 eur
Rückzahlung 05/02/2014  173 eur
Rückzahlung 04/01/2014  173 eur
Abschlußposten  03/31/2014  -190 eur
Rückzahlung 03/03/2014  173 eur
Versicherungsprämie 02/06/2014  -870 eur
Bearb/ Entg 02/06/2014  -240 eur
Zuzählung   02/06/2014  -12000 eur
``````
• You also need to use the size of the regular payment, the timing of payments, and the number of those payments – DJohnM Oct 2 '14 at 16:32
• I'm not familiar with Mathematica, but given a series of dates and cash flows, I would presume you can use an IRR (internal rate of return) calculation. Of course, as the person who borrowed, you aren't the one earning the "return", but rather paying it. To compute the effective interest to the current date, you may need to terminate the series with an artificial entry pretending to repay the entire current balance. Doing this in Microsoft Excel is straightforward and I would expect Mathematica would be, too. – Chris W. Rea Oct 2 '14 at 19:49
• p.s. If you use IRR, you don't need any of the information User58220 mentions. The effective interest rate to date, if that is all you are interested in, should be implied by all the data you have there already. – Chris W. Rea Oct 2 '14 at 19:50
• @ChrisW.Rea: thanks, but how would you exaclty do in Excel? If you post the whole answer next users which will read could find it useful also. – Revious Oct 2 '14 at 20:30
• I'd just find an online loan amortization calculator, put in the principle and period, and then play around with the interest rate until it shows your payment amount. – Eric Gunnerson Oct 3 '14 at 10:15