SOLUTION: Find the time it takes for $610,000 to double when invested at an annual interest rate of 20% compounded continuously

Algebra ->  Finance -> SOLUTION: Find the time it takes for $610,000 to double when invested at an annual interest rate of 20% compounded continuously       Log On


   

Question 1163089: Find the time it takes for $610,000 to double when invested at an annual interest rate of 20% compounded continuously
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The formula for continuous compounding is

A+=+Pe%5E%28rt%29

P is the beginning principal
A is the final amount
r is the annual interest rate
t is the number of years

You know the interest rate; and you know you want the amount to double -- that is, you want A = 2P. So

2P+=+Pe%5E%28rt%29
e%5E%28rt%29+=+2
rt+=+ln%282%29
t+=+ln%282%29%2Fr

Substitute the given interest rate of 20% (0.20) and use a calculator.

Note that the original amount is irrelevant; for a given interest rate, the doubling time is the same whether the original amount is a dollar or a million dollars.