Question

**(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 the interest is is $?

Answer #1

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 future value of a $40,000 annual income stream if it is
invested immediately as it is received into an account paying 10%
interest compounded continuously for 15 years. Round your answer to
the nearest cent.

Find the value of an income stream after 8 years if the rate of
flow is estimated to be $240,000 annually and the income is
deposited at a rate of 6 percent compounded continuously. Round
intermediate answers to eight decimal places and final answer to
two decimal places.

1. A retiree is paid $1200 per month by an annuity. If the
income is invested in an account that earns 9% interest compounded
continuously, what is the future value of the income after ten
years? (Round your answer to two decimal places.)
$ 233536.47 < --- wrong answer
.
2. The winner of a lottery is awarded $7,000,000 to be paid in
annual installments of $350,000 for 20 years. Alternatively, the
winner can accept a "cash value" a one-time...

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

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

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$ =

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.)

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 total value TV of the given income stream and
also find its future value FV (at the end of the given
interval) using the given interest rate. HINT [See Examples 4, 5.]
(Round your answers to the nearest cent.)
R(t) = 30,000, 0 ≤
t ≤ 20, at 4%
TV
=
$
FV
=
$

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