MATHS_Indices and Iogarithms

In the compound interest () formula A = P (1 + R)^a,
(a) if P = 100,000 , r = 8%, n = 5, find the value of A,

Ans:

A = P (1 + R)^a=100,000 (1+8%)^5=146932.8//

(b) if A = 21,003.42, P = 10,000 , n = 5 , find the valiue of r ,

Ans:

A = P (1 + R)^a
21,003.42=10000(1+R)^5
2.100042 = (1+R)^5
=> log 2.100042 = 5 log (1+R)
=> log(1+R)=0.64445596
=>1+R=1.159966898
=>R=16%//

(c) if A = 80957.13, P = 35000, r = 15%, find the value of n.

Ans:

A = P (1 + R)^a
80957.13=35000(1+15%)^n
=>2.095713=(1+0.15)^n
=>log 2.095713 = n log 1.15
=> n = log 2.095713 / log 1.15 =5.3 //

SOLUTIONS :

(a) When P = 100,000 , r = 8% and n = 5,
A = 100,000 (1 + 8%)^5
= 100000 (1.08)^5
= 146932.8077
= 147000

(b) When A = 21,003.42, P = 10,000 and n = 5,
21003.42 = 10000( 1 + r )^5
2.100042 = ( 1 + r )^5
(2.100042)^ 1 / 5 - 1 = r
r = 0.159966898
= 15.996698 %
= 16.0 %

(c) When A = 80957.13, P = 35000 and r = 15%,
80957.13 = 35000( 1 + 15% )^n
80957.13 / 35000 = ( 1.15 )^n
log80957.13 / 35000 = nlog1.15
n = log80957.13 / 35000 / log 1.15
= 6.000000283
= 6.00

ALL ANSWERS ARE CORRECT TO 3 SIG. FIG.

2009-04-04 01:17:32 補充：
n = (log80957.13 / 35000) / (log 1.15)
this form will be better rather than 'n = log80957.13 / 35000 / log 1.15'

2009-04-04 03:46:39 補充：
(a) A = $ 147000