✔ 最佳答案
Let r be the interest rate per annum.
Draw a time line in years.
Steven deposit $20000 at time 0 and deposit $20000 at time 1.
At time 2, he can get $43672.
Note that the first deposit has been invested for 2 years and the second deposit has been invested for 1 year.
20000(1+r)² + 20000(1+r) = 43672
Let x = 1 + r,
20000x² + 20000x - 43672 = 0
2500x² + 2500x - 5459 = 0
(50x - 53)(50x + 103) = 0
x = 53/50 or x = -103/50 (rejected)
r = x - 1 = 3/50 = 0.06 = 6%
The interest rate per annum is 6%.
2013-10-18 20:57:49 補充:
星塵,謝謝你~
如果你將來有機會學 financial mathematics,這個是典型的 annuity-due 類型。
2013-10-18 20:58:29 補充:
那麼你上邊let 的應該是 interest rate = r%, not r.
2013-10-18 21:00:21 補充:
或者我翻譯一下題目。
重點在於 "at the beginning of each year",即是每年的年頭,他都會存款,所以由一開始去到第二年的年尾,他於第一年的年頭和第二年的年頭都有存款。