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:
According to the schedule, the monthly interest repayment is
The total interest is
24*125 = 3000Interest rate calculated from total interest
Interest rate calculated from total payments
15.75% can be considered as the APR
Quoting: APR – Multiple definitions
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:
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.
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%