F5 Mathematics

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。

Another way：

Let the interest rate be r.

20000(1+r%)^2+20000(1+r%)=43672
20000(1+r%)^2+20000(1+r%)-43672=0

let (1+r%) be x.
20000x^2+20000x-43672=0
x=-2.06 (rej) or x=1.06
1+r%=1.06
r%=0.06
r%=6%

∴the interest rate=6%

2013-10-18 20:23:01 補充：
20000x^2+20000x-43672=0 用計算機因式分解

2013-10-18 20:26:14 補充：
方法其實同Masterijk一樣,
只不過let多咗個%......

2013-10-19 17:19:25 補充：
係啵~
咁我下次都唔let%,
費事let錯野......