# Thread: Future Value and Continuous Income Stream

1. ## Future Value and Continuous Income Stream

hmmmm... I actually have solved this problem already but I am a little bit skeptic about the rate used. since the problem says it is in weeks but the interest rate is annually.

2. ## Re: Future Value and Continuous Income Stream

Interest rates are almost always given annually regardless of the other time units in the problem. If you want the weekly rate, you have to convert it.

If you show us what you did, we can check your work.

- Hollywood

3. ## Re: Future Value and Continuous Income Stream

Thanks so much! That's exactly what I was looking for
Btw do you mind clarifying your first sentence? As in, why should you write just (-∞, 0)∪(0, 9) and not x∈(-∞, 0)∪(0, 9)? Thanks again
!!!
EDIT: Or I guess what I mean is, how do you define your variable with interval notation? It seems no one ever says "x" anywhere when they say their answer in interval notatio
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4. ## Re: Future Value and Continuous Income Stream

hmmmm Future Value is represtened as e^(Txrate)Integral of f(x)e^-(ratext)dx
The rate is the rate of interest compounded continuously...
f(x) is the rate of continuous income ...
T is the duration of time since the money was invested.
t is the total time when the interest began being added to the principal. so Principal is continous income flow or f(x) and while it is flowing it is also increasing by the interest so thus the Principal is changing.. Original equation is Integral from 0 to T of f(x)e^(T-t)dx