A bank pays interest at the rate of 11% on $6000 deposited in an account. After how many years will the money have tripled?
The original amount deposited is $6000. The rate of interest is 11%. Now we need to determine how long it takes for the money to triple.
Here we use the formula for compounding of interest as every year interest is also earned on the previous year's interest.
Therefore if the time taken is n years
6000*(1+ .11)^n = 6000*3
cancel 6000 which is common on both the sides.
=> 1.11^n = 3
We can use logarithms here
=> n = log 3 / log 1.11
Therefore $6000 becomes triple or $18000 in 10.5271 years if the rate of interest is 11% every year.
Principle = P = $6000.
Rate of interest: 11%.
If it is simple interest , we require 200% interest to make the principle 300%. So the number of years required = 200/11= 18.1818 years for the amount to triple.
If it is compound interest (annual), then it requires P to become 3P in n years.
Then P(1+11/100)^n = 3P.
Dividing by P, we get:
(1+11/100)^n = 3.
Taking logarithms, we get:
n log(1.11) = log3.
n = log3/log1.11 = 10.5271 years