f.2複利率 (20points) (好少人黎答)(急急急急急急!!!!!!)

1) i) 每期半年, 共3期(18個月/6個月), 每期(半年)利率4% (8%/2)
本利和=$18000*(1+4%)^3=$20247.6
利息=$20247.6-$18000=$2247.6
或直接計利息=$18000{[(1+4%)^3]-1}=$2247.6

ii) 每月一結, 共18期, 每期利率2/3%
直接計利息=$18000{[(1+2/3%)^18]-1}=$2296.9

2) 設b借了$A,
每月一結, 共9期, 每期利率1%
$32811=$A*(1+1%)^9=1.0937$A
$A=$32811/1.0937
$A=$30000
b借了$30000

3) 設c 存了$A,
每3月一結, 共14期(3.5*4), 每期利率1.5%
$1970=$A{[(1+1.5%)^14]-1}=0.2318$A
$A=$1970/0.2318
$A=$8500
c 存了$8500

4) 設年利率為n%
每半年一結, 共2期, 每期利率n%/2
$46305=$42000*(1+n%/22
(1+n%/22=$46305/$42000=1.1025
(1+n%/2)=1.05
n%/2=0.05
n%=0.1=10%
年利率為10%

2007-02-11 19:56:42 補充：
重要公式:本利和 = 本金(1 加 每期利率)^期數

2007-02-12 02:18:08 補充：
4) 第3,4行打漏2個)^, 應為$46305=$42000*(1 n%/2)^2(1 n%/2)^2=$46305/$42000=1.1025

2007-02-12 02:18:40 補充：
$46305=$42000*(1n%/2)^2(1加n%/2)^2=$46305/$42000=1.1025

2007-02-12 02:19:08 補充：
$46305=$42000*(1加n%/2)^2(1加n%/2)^2=$46305/$42000=1.1025

1a.18000X(1+8%/2)^18=36465(corr.to nearest dollars)
b.18000X(1+8%/12)^18=20287(corr.to nearest dollars)
2.Let $b be the money that he borrowed
bX(1+12%/12)^9=32811
b=30000(corr.to nearest dollars)
3.Let $b be the mony that he deposited
bX(1+6%)^3.5-b=1970
b=8708(corr.to nearest dollars)
4.Let r% be the rate
42000X(1+r/12)^6=46305
r=19.6%(corr,to 3 sign. fig)

1)
i) [(1+0.08/2)^3-1]/1.5*100%=8.32%
ii) [(1+0.08/12)^18-1]/1.5*100%=8.47%

2)
d(1+12%/12)^9=32811
d=32811/[(1+12%/12)^9]
d=30000.4

3)
d[(1+6%/4)^(4*3.5) - 1]=1970
d=8500.3

4)
設年利率為r%
42000(1+r%/2)^2=46305
(1+r%/2)^2=1.1025
1+r%/2=1.05
r%=0.1
r=10

1) i) 18000*(1+8%/2)3次
ans: 20247.552

ii) 18000*(1+8%/12)18次
ans: 20286.86286

2) b*(1+12%/12)9次=32811
b=30000

3) c*(1+6%/4)14次 - c=1970
c=8500

4) 42000*(1+r%/2)2次=46305
ans=10%