# 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? – 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

## 2 Answers

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. – 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.

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