A note on the approximate calculation of APR and redemption yields

Approximate formulae for the yield on a transaction involving an initial loan which is repaid by regular level instalments and, possibly, an additional final repayment are derived and applied to consumer credit calculations and to the calculation of redemption yields for fixed-interest securities. The method of approximation takes advantage of the presence of the generating functions of the Bernoulli numbers and of the Bernoulli polynomials and produces surprisingly accurate results over the range of parameter values typically encountered in practice.