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An investment has been growing at a fixed annual rate of 20% since it was first made, no portion of the investment has been withdrawn, and all interest has been reinvested. How much is the investment now worth?
(1)The value of the investment has increased by 44% since it was first made.
(2)If one year ago $600 had been withdrawn, today the investment would be worth 12% less than it is actually now worth
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all interest has been reinvested，表明是年复利增长，问现在的总数是多少？
条件1：从开始到现在，投资增加了44%。设开始时投资额是a, 到现在已经投资了n年， 那么a*(1+20%)^n=a(1+44%)，得出n=2。但是不知道a, 不充分。
条件2：一年前撤资了600。设一年前没撤资前已经投资了b, (b-600)*(1+20%)=88%*b*(1+20%), 可以求出b,
现在的投资额是b*(1+20%), 充分。
nishiki
条件2设现在的投资价值是x ，[(x/1.2)-600]*1.2=x*(1-12%),x=6000
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2022-09-26 09:42:24
680461elv
条件2可以不用管年数了，因为可以直接用未知数b代替之前所有年份投资账户里面的所有钱，再算一年复利即可满足条件的说法，列式(b-600)(1+20%)=（1-22%）b (1+20%)，可以求出b（1+20%），正是所求的内容
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2022-08-13 16:36:40
旮旮
B选项： 条件2 设一年前的本息和为X 则（X-600)*1.2=X*1.2*(1-12%) 得1.2X=6000
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2021-10-27 20:33:21
贾思敏
考点：文字题-利润问题 题干：all interest has been reinvested，表明是年复利增长，复利率是20%，问现在的总投资（原有的投资金额*（1+20%）^n，n是存了多少年）是多少？ 关键是要知道：原有投资金额等于多少？存了多少年？（题干没说多少年，条件也没说多少年，根据题干的意思理解：条件一可以算出2年，条件二按1年来算，这样就很绝绝子，需要小心的一个点！） 条件1：The value of the investment has increased by 44% since it was first made. 从开始到现在，投资增加了44%。设原有的投资金额是a, 到现在已经投资了n年， 那么a*(1+20%)^n=a(1+44%)，得出a*1.22^n=a*1.44，因此n=2。但a未知，不充分。 条件2：If one year ago $600 had been withdrawn, today the investment would be worth 12% less than it is actually now worth（要注意的是条件二默认n=1，one year ago） 一年前取钱取了600。设一年前没取钱之前的原有投资额是b, 那么it is actually now worth是b-600，可以列出以下等式： (b-600)*(1+20%)=（1-22%）*b*(1+20%) 化简可得：b-600=0.78b，不用算出答案，知道b有唯一确定值，就是充分的。充分。
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2021-10-11 14:41:23
击麦700+++
条件2也没说人家是多久开始存的呀，万一是两年前或者是三年前开始存的就多出了一个未知数根本解不出来啊，好奇怪
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2021-09-30 12:16:55
Melody牛回复击麦700+++
说了如果一年前取了600balabala，知道一年前的金额就好了呀
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2021-10-06 18:03:33
715007m
all interest has been reinvested，表明是年复利增长，问现在的总数是多少？ 条件1：从开始到现在，投资增加了44%。设开始时投资额是a, 到现在已经投资了n年， 那么a*(1+20%)^n=a(1+44%)，得出n=2。但是不知道a, 不充分。 条件2：一年前撤资了600。设一年前没撤资前已经投资了b, (b-600)*(1+20%)=88%*b*(1+20%), 可以求出b, 现在的投资额是b*(1+20%), 充分。
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2020-09-29 16:29:14
凡人L
楼上说的不对！尤其根据这个条件y=(1+20%)列出的条件一的式子 人家只说了An investment has been growing at a fixed annual rate of 20% since it was first made一项投资自首次投资以来一直以每年20%的固定速度增长，并没说存的年份！
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2020-09-05 20:32:38
Morton回复凡人L
条件2设的未知数是去年1月1日户头里所有的钱，包括以前以前年度的所有利息，因为是复利，而且题目问得是现在有多少钱，所以可以不用年份了
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2021-04-15 00:18:09
C韵
设原本投资x，现在有y；已知y=(1+20%)x (1) (y-x)/x = 44% →0.2x/x=44% × ； (2) (x-600)(1+20%)=y(1-12%) → 0.32x=720√
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2019-11-13 22:29:28
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