Comparing Present and Accumulated Value of Annuities With different Interest Rates

Assume we have k immediate (due)-annuities with different interest rates. Let i = (i1; i2; :::; ik)and i = (i 1; i 2; :::; i k) be two vectors of interest rates such that i is majorized by i. It’s shown that Σki=1 a nji iΣki=1 a njii as well as Σki=1 s nji iΣki=1 s njii . We also prove the similar results for annuitiesdue.

Keywords:

Arithmetic mean , Majorization , Schur-convex function.