數學題(CONPOUND INTEREST)

For Compound Interest:

Principle + Interest = Principle (1 + interest rate in decimal form)^term
A = P(1 + i)^T

Note: ^T means raised to the power T

Let us make up the question to illustrate compound interest:
How long does it take for a sum of money to grow ten times (say $1000 to become $10000) if the interest rate is 12% per annum and interest is compounded every year?
P = $1000
A = $10000
Interest rate = 12%, i = 0.12 (in decimal form)
T = ?
10000 = 1000 (1 +0.12)^T where T is the term in years
10000/100 = (1.12)^T
10 = (1.12)^T

Taking logarithm on both sides
Log (10) = log (1.12^T)
Log (10) = T log (1.12)
T = log (10) /log (1.12)
T = 1/0.049218022
T = 20.32

The term is 20.32 years

It takes 20.32 years for a sum of money to grow to 10 times the original principal if interest rate is 12% per annum compounded every year.



2011-06-08 03:13:44 補充：
Correction:
10000 = 1000 (1 +0.12)^T
10000/1000 = (1.12)^T
10 = (1.12)^T

Not 10000/100 = (1.12)^T

T = 1In10/In1.12
= 20.32