I need formula to calculate nominal APR from balloon loan with contract fee. The initial data and payment schedule is:

Loan sum: 10 000€

Interest rate per year: 15%

Loan period: 2 years

Payments in year: 12

Contract fee: 150€ (1.5% from loan sum)

Payment schedule:

Payment schedule

  • 4
    15% is the APR. What exactly are you looking for? – Ben Miller May 13 '16 at 15:01
  • You beat me by a few seconds.... – JoeTaxpayer May 13 '16 at 15:02
  • Thank you for the comment. I have specified my question and added contract fee to the payment schedule which I had forgotten previously. What is the APR now and how do you calculate it ? – MulOnPomm May 17 '16 at 9:39

The acronym APR is ambiguous, especially given that the loan in question is denominated in Euros. This site, https://en.wikipedia.org/wiki/Annual_percentage_rate#Multiple_definitions_of_effective_APR, gives definitions for both the US and the EU. From the repayment schedule given, it is clear that:

  1. The lender is charging a nominal interest rate of 15% per year, with monthly compounding, or 1.25% per month. The with monthly compounding should have been included in the specification of the loan; the quoted interest rate of 15% is meaningless without it. The compounding period could only be inferred from the payment schedule.

  2. An single initial deposit of $100, left to earn interest of 1.25% per month compounded monthly for 12 months would grow to 100 x (1.0125)^12 or $116.075. The same $100 left to grow for 1 year at 16.075% compounding annually would grow to the same amount. Thus, the effective annual interest rate for the loan described is 16.075%

  • 1
    This is an interest-only loan. There is no compounding. – Ben Miller May 13 '16 at 16:18
  • If the 15% were paid at year end, it's 15%. But since there are monthly payments, there's an effective rate. Same as compounding – JoeTaxpayer May 13 '16 at 16:41
  • This borrower pays 125 Euros into a 10000 Euro debt each month, and still owes 10000 Euros. How could the lender not be added the interest into the debt each month, the very definition of compounding? – DJohnM May 13 '16 at 17:49
  • @DJohnM - +1 from me, my comment was to Ben, as I trust your's is. I agreed with your math. – JoeTaxpayer May 13 '16 at 18:34
  • @JoeTaxpayer, DJohnM: Okay, thanks for the explanation. – Ben Miller May 13 '16 at 20:21

According to the schedule, the monthly interest repayment is

125 = 10000*15/100/12

The total interest is 24*125 = 3000

Interest rate calculated from total interest

3000/10000/24*12*100 = 15%

Interest rate calculated from total payments

(3000 + 150)/10000/24*12*100 = 15.75%

15.75% can be considered as the APR

Quoting: APR - Multiple definitions

  • Laws vary as to whether fees must be included in APR calculations.

protected by Community Jan 22 '18 at 9:31

Thank you for your interest in this question. Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site (the association bonus does not count).

Would you like to answer one of these unanswered questions instead?

Not the answer you're looking for? Browse other questions tagged or ask your own question.