Implied interest rate calculator
When you are only told the amount lent and the payment to make, this finds the interest rate really charged.
Result
7.42%Rate per year (nominal)
- Rate per period
- 0.6183%
- Effective rate per year
- 7.68%
- Total paid
- 12,000.00
- Interest cost
- 2,000.00
Inputs
- Amount lent
- 10000
- Payment each period
- 200
- Number of payments
- 60
- Payment frequency
- Every month
How it is calculated
We look for the rate i such that amount = payment × (1 − (1 + i)^−n) ÷ i.
Result
Rate per year (nominal)
- Rate per period
- 0.6183%
- Effective rate per year
- 7.68%
- Total paid
- 12,000.00
How it is calculated
- We look for the rate i such that amount = payment × (1 − (1 + i)^−n) ÷ i.
- Numerical solving (Newton’s method, backed by a scan with bisection): it stops when the rate moves by less than 1e−13 per period, and the result is kept only if the gap left is below one millionth of the amount. The rate shown is exact to the rounding.
- Nominal rate = i × periods per year; effective rate = (1 + i)^(periods per year) − 1.
- If no rate gives this result, this is flagged.
Example
10,000 lent, repaid with 60 monthly payments of 200: 0.6183% a month, that is 7.42% a year (7.68% effective); 2,000 of interest.
Good to know
- Equal, regular payments, with no fees or insurance.
- This is not a regulated APR.
Frequently asked questions
What is this tool used for?
When you are only told the amount lent and the payment to make, this finds the interest rate really charged.
How is the result calculated?
We look for the rate i such that amount = payment × (1 − (1 + i)^−n) ÷ i.
What should I check before using the result?
Equal, regular payments, with no fees or insurance.