In this section we will apply the definite integral to three useful analytical tools for business:
The first of these, the future value of an income stream, measures the value of an income stream by calculating the accumulated total of a continuing stream of revenue invested at a continuous rate r over a period of T years. The present value of an income stream is another way of measuring the value of an income stream. The present value is the lump-sum principle that would have to be invested now for a period of T years at a continuous rate of interest r in order to equal the future value of the income stream continually invested at the same rate over the same time T. That is, the bigger the future value of the stream, the more up-front principal P would have to be invested now at the same rate r in order to come out the same as the future value after T years.
Consumers’ and suppliers’ surplus help management evaluate the unit price of a commodity, i.e. whether it is too low or too high or just about right for the market.