求助advanced数学第127题

owen在杭州 · 发表于 2020-2-5 01:34:28

A bank account earned 2% annual interest, compounded daily, for as long as the balance was under $1,000, starting when the account was opened. Once the balance reached $1,000, the account earned 2.5% annual interest, compounded daily until the account was closed. No deposits or withdrawals were made. Was the total amount of interest earned at the 2% rate greater than the total amount earned at the 2.5% rate?
The account earned exactly $25 in interest at the 2.5% rate.
2. The account was open for exactly three years.

新出的难题数学题里第127题，答案选C，我自己想的解题过程很复杂很复杂，应该是想偏了，求大神指导，能给出详细的解题过程最好了！跪谢！

DD_c · 发表于 2020-2-5 02:34:11

（1）balance到1000后利息是25元：
穷逼存1元, 吃几百年利息到1000, 然后吃不知道多久到1025, 2%>2.5%利息 (1000>25);
高富帅直接存999.9元，拿到1025，2%<2.5%利息（0<25）
（2）开了三年
穷逼存1元, compound daily也不可能三年利息把本金翻1000倍... 2%>2.5%利息 (某数>0)
高富帅直接存999.9元，拿到1000+，2%<2.5%利息（0<某数）

（1）（2）已知时间，已知利率，已知总利息，本金肯定可求。知道本金，那肯定就知道每个阶段利息了，所以可比

owen在杭州 · 发表于 2020-2-7 16:19:39

DD_c 发表于 2020-2-5 02:34
（1）balance到1000后利息是25元：
穷逼存1元, 吃几百年利息到1000, 然后吃不知道多久到1025, 2%>2.5%利息 ...

这回懂了谢谢！！！

求助advanced数学第127题

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