問題如下：
Ian has deposited $3800 into the bank and interest is compounded half-yearly.If the interest earned after one year's deposite is$389.5,find the compound interest rate per annum.
謝謝！
有D數學題不懂，如可答，有10點！
2007-07-26 3:39 am
回答 (2)
2007-07-26 4:44 am
✔ 最佳答案
Let the compound interest rate be r%.There are 2 half years in 1 year.
3800 ( 1 + r% / 2 )^2 - 3800 = 389.5
3800 ( 1 + r% / 2 )^2 = 4189.5
( 1 + r% / 2 )^2 = 1.1025
1 + r% = 1.05
r% = 0.05
r = 5
Hence the interest rate p.a. is 5%.
2007-07-25 20:45:33 補充：
Sorry that I have forgotten the r% / 2 and so the answer should be 10%.
參考: My Maths Knowledge
2007-07-26 10:01 am
Let the compound interest rate be r%. For half-yearly compound interest, the number of periods per year is 2. So we can set the equation
3800 * (1 + r% / 2) ^ 2 - 3800 = 389.5
(1 + r/200)^2 = (389.5 + 3800) / 3800 = 1.1025
1 + r/200 = sqrt(1.1025) = 1.05
r = (1.05 - 1) * 200 = 0.05 * 200 = 10
Therefore, the compound interest rate per annum is 10%.
3800 * (1 + r% / 2) ^ 2 - 3800 = 389.5
(1 + r/200)^2 = (389.5 + 3800) / 3800 = 1.1025
1 + r/200 = sqrt(1.1025) = 1.05
r = (1.05 - 1) * 200 = 0.05 * 200 = 10
Therefore, the compound interest rate per annum is 10%.
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原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20070725000051KK04476