am that will be providing income in the future. The present value is useful in deciding when to replace machinery or what newequipment to select. When the notion of the present value is extended to an infinite time interval, the result is called the capital value of the income stream and is given by ????????????=∫?(?)⋅?−??ⅆ?? Suppose that an organization wants to establish a trust fund that will provide acontinuous income stream with an annual rate of flow at time t given by f(t) =10 000.If the interest rate r=0.01.Mper year, compounded continuously, find thecapital value of the fund when they plan to operate a) 3 years, b) forever.
Find the sum M=p+q+r.
M=8
The definite integral can be used to find the total income over a fixed number of years from a continuous income stream. The definite integral can also be used to find the present value -the value today of a continuous income stream that will be providing income in the future. The present value is useful in deciding when to replace machinery or what newequipment to select. When the notion of the present value is extended to an infinite time interval, the result is called the capital value of the income stream and is given by
????????????=∫?(?)⋅?−??ⅆ??
Suppose that an organization wants to establish a trust fund that will provide acontinuous income stream with an annual rate of flow at time t given by f(t) =10 000.If the interest rate r=0.01.Mper year, compounded continuously, find thecapital value of the fund when they plan to operate a) 3 years, b) forever.
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