在线求一道英语数学题.Compound Interest.A fortunate algebra student wants to invest $1,000,000 in a tax-free fund.If she hopes to double her investment in 8 years,What interest rate mush she seek if her account is compounded monthly?Give your answer in percent and correct to the nearest decimal place.现在我知道答案 r约等于 8.7%不过我不会算..这个公式对吗?2x1,000,000=1,000,000(1+r/12)^8x12.怎么计算呢?
问题描述：
在线求一道英语数学题.Compound Interest.
A fortunate algebra student wants to invest $1,000,000 in a tax-free fund.If she hopes to double her investment in 8 years,What interest rate mush she seek if her account is compounded monthly?Give your answer in percent and correct to the nearest decimal place.
现在我知道答案 r约等于 8.7%
不过我不会算..这个公式对吗?
2x1,000,000=1,000,000(1+r/12)^8x12.
怎么计算呢?
答
本题中让算的是月利率，不可能那么高的。按复利计算法求（就是所谓“利滚利”）。
2x1,000,000=1,000,000*(1+rm)^（12x8）化简得
(1+rm)^96=2
1+rm=2^(1/96)
rm=2^(1/96)-1=0.0072=0.72%
如果计算年利率ra，同样有
2x1,000,000=1,000,000*(1+ra)^8化简得
(1+ra)^8=2
1+ra=2^(1/8)
ra=2^(1/8)-1=0.0905=9.05%
答
英文看不懂
答
compounded 表示利息按复利计算 要用指数公式
设年复利为r 则e^8r=2 推出r=8.7%