Compound Interest Formula

From Open Risk Manual

Definition

Compound interest is the cumulation of interest to the principal sum of a loan or deposit

Formula


CI = \left[ \prod_{i=1}^{d_b} (1 + \frac{r_i \times n_i}{N}) - 1 \right] \ \times \frac{N}{d_c}

Where

  • d_b is the number of business days in the interest period
  • d_c is the number of calendar days in the interest period
  • r_i is the interest rate applicable on business day i
  • n_i is the number of calendar days for which rate ri applies (on most days, ni will be 1, but on a Friday it will generally be 3, and it will also be larger than 1 on the business day before a holiday).
  • N is the market convention for quoting the number of days in the year.

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