Interest Rates

Quick Version

Curo Calculator is designed to solve unknown values using one of three rates of interest: a Nominal Annual Rate (NAR), an Effective Annual Rate (EAR), and an Annual Percentage Rate (APR). It also solves for an unknown interest rate when all other inputs are provided.

The type of interest used in a calculation is determined by your choice of day count convention. See Core-Concepts > Day Count Conventions for details on supported conventions. When selecting a convention on the calculator input screen, you’ll notice the label of the interest rate input field updates to reflect the type of interest that will be used.

  • Nominal Annual Rate (NAR) - The basic interest rate over a year without considering compounding or inflation.
  • Effective Annual Rate (EAR) - Takes into account the effect of compounding within the year, giving a more accurate annual rate.
  • Annual Percentage Rate (APR) - Similar to EAR in calculating days with reference to the initial drawdown but mandated by law to reflect the true cost of borrowing, including fees and other charges, but not considering compounding frequency within the year.

Deep Dive Version

Nominal Annual Rate (NAR)

Definition:
The NAR is the stated interest rate for a year, before adjustments for compounding or inflation. It’s the simplest form of expressing interest.

Example:
If a loan has a NAR of 5%, this means you would pay 5% of the principal in interest over one year, if no compounding is applied.

$$ Interest = Principal \times \frac{NAR}{100} $$

Effective Annual Rate (EAR)

Definition:
The EAR accounts for the effects of compounding within the year. It’s the actual rate you would pay or earn annually, considering how often interest is compounded.

Example:
For a nominal rate of 5% compounded quarterly:

$$ EAR = \left(1 + \frac{0.05}{4}\right)^4 - 1 \approx 5.095\% $$

Annual Percentage Rate (APR)

Definition: The APR is a standardised measure of the cost of borrowing, mandated by law to reflect not just the interest rate but also other charges like fees, providing a more comprehensive view of borrowing costs. However, unlike NAR, it does not account for the frequency of compounding within the year.

Example: Consider a one-year loan of €1,000 where:

  • The Nominal Annual Rate (NAR) is 5%.
  • The loan has an origination fee of 1% (€10 added to the cost).
  • Interest compounds monthly, but for simplicity, we’ll calculate APR assuming annual compounding for comparison with regulatory standards.

Calculating APR:

  1. Total Interest: Based on NAR, the interest would be €1,000 * 5% = €50.
  2. Total Fees: The origination fee adds €10.
  3. Total Cost of Borrowing: €50 (interest) + €10 (fee) = €60.

For APR:

  • Simplified APR Calculation (assuming annual compounding for regulatory purposes):

    $$ APR = \frac{Total Cost of Borrowing}{Principal} \times 100 $$ $$ APR = \frac{60}{1,000} \times 100 = 6\% $$

  • This means, although the NAR is 5%, when you include the fee, the APR effectively becomes 6%, providing a clearer picture of the loan’s cost without considering the compounding effect within the year.