关于financial management的问题

来源：学生作业帮编辑：作业帮分类：英语作业时间：2024/05/09 11:09:06

关于financial management的问题
You plan to make a series of monthly deposits for 35 years to save for your retirement,with the first deposit made today and the last deposit at the date of your retirement.A month after your retirement from work,you would start withdrawing $2000 a month for the next 30 years.Interest rates are 6% per annum compounded monthly.What is the amount of the monthly deposit you must save during your 35 years of working life?
或者要套用的公式.不要直接给答案,

分析：以retirement那天为分水岭,以后每月尾取$2000=Payment,取30年,360月=n,年利率6%,月利率0.5%=r
带入ordinary annuity公式可求retirement那天的present value=P[1-(1+r)^-n]/r=333,583.23
这个‘present value’就是今天的future value,已知n’=35*12=420,月利率=0.5%,唯一要注意的是今天就存钱,所以是月头存钱,应选annuity due的公式,Payment=FVdue*i/(1+i)[(1+i)^n-1]=232.98
再问：好吧，但是最后那个公式我没看懂- -如果不麻烦的话请详解- -谢谢
再答： ordinary annuity的future value=Payment[(1+i)^n-1)]/i 如果能理解上面这个公式， annuity due不一样的地方是每一个payment都比ordinary annuity多一个compound period,因为annuity due是月头付，ordinary annuity是月尾付，多了一个月的利息，所以future value due的公式为FVdue=Payment(1+i)[(1+i)^n-1)]/i 变形之后，Payment=FVdue*i/(1+i)[(1+i)^n-1]

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