基金使用计划模型

Model of using funds

本文为了提高每年的奖金额采取了最佳的存款及购买国库券的方法 ,把总基金分为n部分 ,n - 1部分的本息作n - 1年的奖金 ,第n部分的本息等于原基金数额与最后一年奖金之和 ,选择存款期限或购买国库券使每一部分到期利息尽可能最高。根据每年要求奖金数额大致相同 ,且第三年比其它年多 2 0 %的要求 ;给出各部分基金与利息、每年奖金及总金额的关系式 ,解得每年的奖金额与各部分基金数额的计算表达式。模型一只考虑存款不考虑买国库券 ,模型二同时考虑存款与买国库券。若总基金为 50 0 0万元 ,n =1 0年时 ,根据模型一、二得如下结果 :1 .只考虑存款不买国库券 ,则第三年奖金为 1 2 9.0 62 9万元 ,其它年为 1 0 7.552 4万元 (不考虑校庆每年基金 1 0 9.81 69万元 )。 2 .可存款也可购买国库券则第三年奖金为 1 53 .2 359万元 ,其它年为 1 2 7.6967万元 (不考虑校庆每年基金 1 30 .4383万元 )。

This paper gives a optimum model of using funds. The gross funds be seprated into n parts, the n-1 parts and their's intrest be used for prizes of n-1 years , the sum of the last part and it's intrest is the sum of the original gross funds and the last year's prize . The methed of sepration ?￠ terms of depositing money and terms of purchasing treasury bonds are selected for obtaining the most gross intrest under the given condition . Equations are given among each part funds ?￠each year's prize and the gross funds according to given intrest rate ?￠selected deposit terms and the request that each year' s prize be about equal . The calculation formulas of each part funds are obtained from the above equations .Model 1 conside only depositing money without purchasing treasury bonds .Model 2 conside not only depositing money but also purchasing treasury bonds. Provided that the gross funds is 50 million yuan and n is 10 years , the following conclusions is obtained . According to model 1, the third year's prize is 1.290629 million yuan , other year's prize is 1.075524 million yuan , if celebrating school's birthday be not consided ,each year's prize is 1.098169 million yuan . According to model 2, the third year's prize is 1.532359 million yuan , other year's prize is 1.276967 million yuan , if celebrating school's birthday be not consided ,each year's prize is 1.304383 million yuan .