Consider an income stream of R t dollars per year earning

Last updated: 3/2/2023

Consider an income stream of R t dollars per year earning interest at the rate of r per year compounded continuously The present value of the income stream R t over a term of T years is T R t e t dt PV When the interval of time is infinite we refer to the present value as the capital value of the income stream Notice that the integrand is a form of the continuous exponential model which can be used to model any type of continuous growth or decay depending on the sign of the exponent and is thus regarded as a common and widely applicable model 1 A company is considering expanding their production capabilities with a new machine that costs 95 000 and has a projected lifespan of 8 years They estimate the increased production will provide a constant 12 500 per year of additional income The income stream can earn 0 6 per year compounded continuously Should the company buy the machine 2 Suppose that an organization wants to establish a trust fund that will provide a contin uous income stream with an annual rate of flow at time t given by R t 10 000 If the interest rate remains at 8 compounded continuously find the capital value of the fund