1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: DE - Continuously Compounded Interest

  1. Sep 29, 2010 #1
    1. The problem statement, all variables and given/known data
    A new savings account with an initial balance of zero is made. You save money continuously, at a rate of $500 per month. Also, every month you plan to increase this rate by $5. you've found a bank account that pays continously compounded interest at a rate of 8% per year. Estimate how long it will take for you to save one million dollars.

    2. Relevant equations

    (dS/dt)= rS+k

    3. The attempt at a solution
    I decided to take care of the saving rate first: since my interest is per year I decided to convert the savings to a yearly rate as well where k=500*12=6000, then I had to take care of the increments so I write it as 6000+60t where 60 is found by 5*12, and the t is in years so that every year 60$ are added to the initial saving rate.

    I then tried to use the formula: S(t) = S(initial)*e^rt + [(k+60t)/r][(e^rt)-1)]
    I subbed in my values, and 1 million for S(t) but the problem is that I can't isolate for t and always end up having e^0.08t - t = some number.

    Is there a different way I should approach this problem?
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted