Question

39. Suppose a continuous income stream has an annual rate of flow given by: f(t) = 5000e^(-.01t). If the interest rate is 7%, compounded continuously, create the integral to solve: a) The Total Income for the next 5 year

b) Present Value for the next 5 year

c) Future Value 5 years from now

Answer #1

Suppose that a printing firm considers its production as a
continuous income stream. If the annual rate of flow at time
t is given by
f(t) =
91.5e−0.8(t + 3)
in thousands of dollars per year, and if money is worth 8%
compounded continuously, find the present value and future value
(in dollars) of the presses over the next 10 years. (Round your
answers to the nearest dollar.)
present value$ =
future value$ =

A business is planning to purchase a piece of equipment that
will produce a continuous stream of income for 5 years with rate of
flow f(t) = 7,000. If the continuous income stream earns 6.65%,
compounded continuously, what single deposit into an account
earning the same interest rate will produce the same future value
as the continuous income stream? (This deposit is called the
present value of the continuous income stream.)
1) What is the future value of the...

An investment produces a continuous income stream at the rate of
?(?) = 3000 − 50? dollars per year at time ?. If the prevailing
annual interest rate remains fixed during the next 6 years at 5%
compounded continuously, what is the present value of the
investment over the next 6 years?

find the accumulated present value of the following continuous
income stream at rate R(t), for the given time T and interest rate
k, compounded continuously. R(t)=.06t+400, T=10, k=8

Find the accumulates present value of the following continuous
income stream at rate R(t), for the given time T and interest
rate k, compounded continuously
R(t)=0.01t+100, T=10, k=4%
Round to nearest cent as needed

An heiress receives an income stream from a will at a rate
of
f(t) =
40,000e0.023t
dollars per year.
She invests this income and earns 4.7% interest (compounded
continuously). (Round your answers to two decimal places.)
(a) What is the future value of the income after ten
years?
$
(b) Compute the present value of the income over a ten year
period.
$

Find the present value P of a continuous income flow of
c(t) dollars per year using
P =
t1
c(t)e−rt dt,
0
where t1 is the time in years and r
is the annual interest rate compounded continuously. (Round your
answer to the nearest dollar.)
c(t) = 100,000 + 4000t, r = 5%, t1 = 8

Find the interest earned at 6.25% interest rate compounded
continuously for 4 years, of the continuous income stream with rate
of flow f(t)=1650e-.02t

Future Value of an Investment
An investment is projected to generate a continuous revenue
stream at the rate of
R(t) =
50,000e0.03t
dollars/year for the next 3 years. If the income stream is
invested in a bank that pays interest at the rate of
5.5%/yearcompounded continuously, find the total accumulated value
(in dollars) of this income stream at the end of 3 years. (Round
your answer to the nearest dollar.)

(A) Find the present and future value of an income
stream of $9000 per year for a period of 10 years if the interest
rate, compounded continuously, is 2% .
Round your answers to two decimal places.
Present Value = $?
Future Value = $?
(B) How much of the future value is from the income
stream? How much is from interest?
Round your answers to two decimal places.
The amount from the income stream is $?
The amount from...

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