Logarithmic Question (5m)

principal + interest formula:
A = P*(1+r%)^n

Then,
P=10000
A=10500
r=1.2%/4 = 0.3%

Therefore,

10500 = 10000 x (1.003)^n
=> 10500/10000 = (1.003)^n
=> 1.05 = (1.003)^n

taking log both sides,

implied that

log 1.05 = log (1.003)^n
by logarithmic properties,
implied that
log 1.05 = n log (1.003)
n = log 1.05 / log (1.003)
n = 16.28
As required that the internet more than 500,
n = 17.

As computing in quarterly,
16.28 quarters mean 17 x 3 month
=> the time for the principal to accumulate $500 interest is 51 months or 17 quarters.

2010-07-13 14:49:52 補充：
misstyped
>>As required that the INTERNET more than 500,

As required that the INTEREST more than 500,

Every time the compound interest is calculated, the amount is multiplied by a factor of 1 + 1.2/(100 x 4) = 1.003

Now, suppose that n times of compounding is needed, to obtain an interset of at least $500, the amount should be at least $10500, i.e.

10000 x 1.003n >= 10500

1.003n >= 1.05

n log 1.003 >= log 1.05

n >= 16.3

Hence n = 17, i.e. at least 17 times of compounding is needed.

Therefore, 51 months are needed at least.