This tells us that after about hours(around minutes)the populationof the bacteriawill doublein
number.
CompoundInterest
Investorsand bankersdependon compoundinterestto increasetheir investment.Traditionally, banksadded
interestafter certainperiodsof time,suchas a monthor a year, and the phrasewas “the interestis being
compoundedmonthlyor yearly.” With the adventof computers,the compundingcouldbe donedaily or even
moreoften.Our exponentialmodelrepresentscontinuous,or instantaneous,compounding,and it is a good
modelof currentbankingpractices.Our modelstatesthat
where is the initialinvestment(presentvalue)and is the futurevalueof the investmentafter time
at an interestrate of The interestrate is usuallygivenin percentageper year. The rate mustbe converted
to a decimalnumber, and mustbe expressedin years.The examplebelowillustratesthis model.
Example3:
An investorinvestsan amountof and discoversthat its valuehas doubledin years.Whatis the
annualinterestrate that this investmentis earning?
Solution:
We use the exponentialgrowthmodelfor continuouslycompoundedinterest,
Thus
The investmenthas grownat a rate of per year.
Example4:
Goingbackto the previousexample,how long will it take the investedmoneyto triple?
Solution: