1.何先生在一家銀行儲蓄$50000,年利率9.5%,每年以複利息計算一次。2年後,年利率減至8%。問該筆儲蓄在第5年年底是多少?[取答案準確至最接近的$0.1。]
2.一棵樹的高度穩定地以每年2%的率增長。若現在該棵樹高3米,求在以下時間,該棵樹的高度。
(a)2年後
(b)3年前
[取答案準確至最接近的0.01米。]
3.把$23400以年利率5%存放73日,求以單利息計算的利息。(提示1年=365日)
4.黃先生以R%的年利率把玩20000存入銀行,以複利息計算,每季計息一次。若存首6個月的月底他所得的利息是$1218,求
(a)R
(b)在第一季年年底的本利和。
[取答案準確至最接近的$0.1。]
功課問題;? [數學] ( 急x100)
2008-10-12 11:31 pm
回答 (2)
2008-10-13 12:40 am
✔ 最佳答案
1.考慮最初 2 年：
R = 9.5%
n = 2
P = $50000
2 年後的本利和 = P x (1 + R%)n
2 年後的本利和 = $50000 x (1 + 9.5%)2
考慮最後三年：
R = 8%
n = 3
P = $50000 x (1 + 9.5%)2
最後本利和 = P x (1 + R%)n
最後本利和 = $50000 x (1 + 9.5%)2 x (1 + 8%)3
最後本利和 = $50000 x (1.095)2 x (1.08)3
最後本利和 = $75521.3
=====
2.
(a)
R = 2
n = 2
P = 3 米
A = P x (1 + R%)n
A = (3 米) x (1 + 2%)2
A = (3 米) x (1.02)2
A = 3.12 米
答：2 年後樹高 = 3.12 米
(b)
R = 2
A = 3
n = 3
A = P x (1 + R%)n
3 = P x (1 + 2%)3
P = 3/(1.02)3
P = 2.83 米
答：3 年後樹高 = 2.83 米
=====
3.
P = $23400
R = 5
n = 73/365
單利息 = P x n x R%
單利息 = $23400 x (73/365) x 5%
單利息 = $234
=====
4.
(a)
每季利率 = (R/4)%
n = 2
P = $20000
20000 x [1 + (R/4)%]2 - 20000 = 1218
20000 x [1 + (R/4)%]2 = 21218
[1 + (R/4)%]2 = 1.0609
1 + (R/4)% = 1.03
(R/4)% = 0.03
R/4 = 3
R = 12
(b)
在第一年年底的本利和
= $20000 x [1 + (12/4)%]4
= $20000 x (1.03)4
= $22510.2
=
2008-10-12 16:40:47 補充：
2(b) 的答案應是 3 年前樹高。
2008-10-13 1:25 am
1,
50000 x (1+9.5%)^2 x (1+8%)^3
=50000 x 1.095^2 x 1.08^3
=50000 x 1.199025 x 1.259712
=75521.3
2,a
3 x (1+2%)^2
=3x1.02^2
=3x1.0404
=3.12
b
3 x (1+2%)^3
=3x1.02^3
=3x1.061208
=3.2
3,
23400x(73x0.05/365)
=23400x0.01
=234
4,a
20000x(1+R%/4)^2-20000=1218
20000x(1+R%/4)^2=21218
(1+R%/4)^2=1.0609
1+R%/4=1.03
R%/4=0.03
R%=0.12
R=12
b
20000x(1+12%/4)
=20000x(1+0.03)
=20000x1.03
=20600
50000 x (1+9.5%)^2 x (1+8%)^3
=50000 x 1.095^2 x 1.08^3
=50000 x 1.199025 x 1.259712
=75521.3
2,a
3 x (1+2%)^2
=3x1.02^2
=3x1.0404
=3.12
b
3 x (1+2%)^3
=3x1.02^3
=3x1.061208
=3.2
3,
23400x(73x0.05/365)
=23400x0.01
=234
4,a
20000x(1+R%/4)^2-20000=1218
20000x(1+R%/4)^2=21218
(1+R%/4)^2=1.0609
1+R%/4=1.03
R%/4=0.03
R%=0.12
R=12
b
20000x(1+12%/4)
=20000x(1+0.03)
=20000x1.03
=20600
收錄日期: 2021-04-23 23:08:12
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20081012000051KK01305