# Comparing present and accumulated value of annuities with different interest rates

Document Type : Research Paper

Author

Department of Statistics, Faculty of Science, University of Kurdistan, Sanandaj, Iran

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

### History

• Receive Date: 26 June 2019
• Revise Date: 26 August 2019
• Accept Date: 26 July 2019