Future value and present value of an income stream
Future value and present value of an income stream Suppose that we have a stream of income which is accrued continuously. (An `income stream'.) Furthermore, we put this income into an account, and it then accrues interest.
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Future value and present value of an income stream Suppose that we have a stream of income which is accrued continuously. (An `income stream'.) Furthermore, we put this income into an account, and it then accrues interest. We'd like to know the future value at some time T . (This is how much the income plus interest is worth after time T .)
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Suppose that money is being transferred continuously into an account over a time period 0 t T . Suppose that the rate of this income is given by a function f (t), and suppose that the account earns an interest rate of r (compounded continuously). The future value of the income stream over the term T is:
FV = erT T f (t)e-rT dt = T f (t)er(T -t)dt
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0
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The Present Value
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The Present Value Suppose that we have a continuous stream of income with rate f (t) and interest rate r, just like in the above situation.
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