@article { author = {Fathi Manesh, Sirous}, title = {Comparing present and accumulated value of annuities with different interest rates}, journal = {Computational Methods for Differential Equations}, volume = {7}, number = {Issue 4 (Special Issue)}, pages = {621-625}, year = {2019}, publisher = {University of Tabriz}, issn = {2345-3982}, eissn = {2383-2533}, doi = {}, abstract = {Assume we have $k$ immediate (due)-annuities with different interest rates. Let ${\bf i}=(i_1,i_2,...,i_k)$ and ${\bf i^*}=(i^*_1,i^*_2,...,i^*_k)$ be two vectors of interest rates such that ${\bf i^*}$ is majorized by ${\bf i}$. It's shown that sum of present and accumulated value of annuities-immediate with interest rate ${\bf i}$ is grater than sum of present value of annuities-immediate with interest rate ${\bf i^*}$. We also prove the similar results for annuities-due.}, keywords = {Arithmetic mean,Majorization,Schur-convex function}, url = {https://cmde.tabrizu.ac.ir/article_9212.html}, eprint = {https://cmde.tabrizu.ac.ir/article_9212_2084fca9938317ba53a836d46dab28d0.pdf} }