兩條 s1 Math per cent question!

a)投資$40000,以單利息計算,年利率3.6%,問要用多少年時間令本利和變為$43600?
let it take n years for the amount to become$43600
40000+40000*3.6%*n=43600
1440n=3600
n=2.5
it take 2.5 years.
b)suki將$8000存入銀行,以單利息計算若他在9個月後會等到本利和$8360,求年利率
let r% be the interest rate per annum.
8000+8000*r%*(3/4)=8360
6000r%=360
r%=0.06=6%
interest rate=6%

a)計算方法如下:
因為interest=investment X(rate of interest Xtime)
根據這條公式,你substitue返d value,
i.e. interest=43600-40000
investment=40000
rate of interest=3.6%
time=n(n is any real number)

i.e.條式就是43600-40000=40000X(3.6%Xn)
3600=40000X(3.6%X n)
3600/40000=40000/40000(3.6% X n)
0.09=0.036X n
0.09/0.036=n
n=2.5
但因為2.5不是整數,所以要到第3年才可以拿到$43600(如果題目寫明一年才能收到一次利息的話,而不是像下面那條可以用月計)


b)其實這條跟上面那條差不多,都是用回那條公式
interest=investment X(rate of interest Xtime)
i.e. interest=8360-8000
investment=8000
rate of interest for 1 year=n
time =9 months/12months(=1 year) =3/4
i.e.條式就是8360-8000=8000 X(n X 3/4)
360=8000 X(n X3/4)
360/8000=8000/8000 X( n X3/4)
0.045=3n/4
0.045 X 4=3n
0.18=3n
n=0.18/3
n=0.06
n=6%
所以一年的利息是6%

part a)
let t be the no. of years.
$40000+$40000(3.6%)(t)=$43600 $1440(t)=$3600
(t)=$3600/$1440
(t)=2.5 years

part b)
let R5 be the interest rate per annum.
$8000+8000(R%)(9/12)=$8360 (P.S. 9/12 =9 months over 1 year)
$6000(R%)=$360
R/100=0.06
R=6%