董先生在25歲生日時將$10000存入銀行,又在26歲生日時存入$9000。銀行是按年以年利率r%計算複利息,而他在27歲時所得的本利和為$22000。求r。
已知答案是10。
需要詳細步驟！！！
4
數學問題:求年利率
2009-12-27 8:17 pm
回答 (2)
2009-12-27 8:30 pm
✔ 最佳答案
[10000x(1+r%)+9000]x(1+r%)=2200010000x(1+r%)2+9000(1+r%)=22000
10000x(1+r%)2+9000(1+r%)-22000=0
10(1+r%)2+9(1+r%)-22=0
[(1+r%)+2]=0 或 [10 (1+r%)-11]=0
1+r%=-2(捨去) 或 1+r%=11/10
∴r%=0.1
r=10
2009-12-27 8:31 pm
25歲存$10000到 26 歲(1年)得 : 10000 * (1 + r%)
26歲再存$9000,即戶口有 10000 * (1 + r%) + 9000
27歲時(1年後) 有 :
[10000 * (1 + r%) + 9000] * (1 + r%) = 22000
10(1+r%)^2 + 9(1 + r%) = 22
10(1 + r%)^2 + 9(1 + r%) - 22 = 0
[10(1+r%) - 11] [(1+r%) + 2] = 0
(1+r%) = 11/10 or (1+r%) = - 2(捨去)
r% = 11/10 - 1 = 1/10 = 10%
r = 10
26歲再存$9000,即戶口有 10000 * (1 + r%) + 9000
27歲時(1年後) 有 :
[10000 * (1 + r%) + 9000] * (1 + r%) = 22000
10(1+r%)^2 + 9(1 + r%) = 22
10(1 + r%)^2 + 9(1 + r%) - 22 = 0
[10(1+r%) - 11] [(1+r%) + 2] = 0
(1+r%) = 11/10 or (1+r%) = - 2(捨去)
r% = 11/10 - 1 = 1/10 = 10%
r = 10
收錄日期: 2021-04-21 22:06:07
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20091227000051KK00455