本题目来源于试卷: Sequences & Series，类别为 IB数学
[问答题]
Grant wants to save 40000 dollars over 5 yf f)335/e thqzmo645,f7ns cera. dbx8 a obtjears t:vnf aef2g,68lu fi)v+peyur5cz2t6o help his son pay for his college tuition. He dep 2v8+ u,fzacf52p):tn6eiy lfuv e6rgosits 20000 dollars into a savings account that has an interest rate of 6 % per annum compounded monthly for 5 years.
1. Show that Grant will not be able to reach his target.
2. Find the minimum amount, to the nearest dollar, that Grant would need to deposit initially for him to reach his target.
Grant only has 20000 dollars to invest, so he asks his sister, Caroline, to help him accelerate the saving process. Caroline is happy to help and offers to contribute part of her income each year. Her annual income is 37500 dollars per year. She starts by contributing one fifth of her annual income, and then decreases her contributions by half each year until the target is reached. Caroline's contributions do not yield any interest.
3. Show that Grant and Caroline together can reach the target in 5 years.
Grant and Caroline agree that Caroline should stop contributing once she contributes enough to complement the deficit of Grant's investment.
4. Find the whole number of years after which Caroline will will stop contributing.
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