Compound Interest

Question

^{How long will it take for $10,000 to triple in value at 7.5% annual interest compounded continuously?}

^{1.) Using the model    A(t)=Pe^rt   show your initial set-up with all known values substituted.}

 

^{2.) Give the exact answer, as a fraction in terms of an appropriate log.}

 

^{3.) Give the approximate answer to the nearest tenth of a year.}

Answer 1

A = Pe^rt

$30,000=$10,000e^.075t divide by $10,000

3 = e^0.075t take natural logs of both sides

ln3 = .075t divide by 0.075

t = ln3/0.075 years = exact solution

= about 14.6482 years =14.6 years rounded to nearest 1/10 of a year

it takes the same amount of time to triple any amount of money. $10,000 or any amount