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

2 thoughts on “Calculate APR from balloon loan

  1. Chris Degnen

    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.
  2. DJohnM

    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%

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