# Calculate APR from balloon loan

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

• 15% is the APR. What exactly are you looking for? May 13, 2016 at 15:01
• You beat me by a few seconds.... May 13, 2016 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 ? May 17, 2016 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%

• This is an interest-only loan. There is no compounding. May 13, 2016 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 May 13, 2016 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? May 13, 2016 at 17:49
• @DJohnM - +1 from me, my comment was to Ben, as I trust your's is. I agreed with your math. May 13, 2016 at 18:34
• @JoeTaxpayer, DJohnM: Okay, thanks for the explanation. May 13, 2016 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.