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Your answer (A) is closer to what I want but not quite. Let me give 2 examples: 1st) (easier problem) Suppose that I start an IRA with an initial investment of $1000 and I want to know how much money I will have in 10 years or 20 years given an expected rate of return. I know the formula to use if I know how long it takes for my money to double:
Final value=initial value * 2^(time elapsed/doubling time)--- I think that this is an equivalent formula to yours for (A).

2nd) (and the one that I am trying to find a formula for) Suppose that I start an IRA with an initial investment of $1000 and every year I add $3000 more to it. What formula can I use to determine how much the IRA will be worth in a certain number of years given an expected rate of return. Also, in this case I would like to use percent expected return per year rather than doubling time. With the formula that you gave (answer A) I could do this by iterative means-calculating how much I earned in interest and adding my new annual investment and starting over with this as my initial value but I would like to avoid the brute force method if possible.

Thanks again,
Carson
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