SOLUTION: Suppose $9,200 is invested in an account at an annual interest rate of 2.5% compounded continuously. How long (to the nearest tenth of a year) will it take the investment to doubl

Algebra ->  Average -> SOLUTION: Suppose $9,200 is invested in an account at an annual interest rate of 2.5% compounded continuously. How long (to the nearest tenth of a year) will it take the investment to doubl      Log On


   

Question 1116509: Suppose $9,200 is invested in an account at an annual interest rate of 2.5% compounded continuously. How long (to the nearest tenth of a year) will it take the investment to double in size?
Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


The amount is irrelevant; whatever the amount is it will double in the same amount of time.

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

We want the final amount A to be twice the original amount P; the equation is then

e%5E%28rt%29+=+2

The given interest rate is 2.5% = .025, so

e%5E%28.025t%29+=+2
.025t+=+ln%282%29
t+=+ln%282%29%2F.025+=+27.726 to 3 decimal places.

Answer: the amount will double in about 27.726 years.