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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
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