Question

The function f(x)=900 represents the rate of flow of money in dollars per year. Assume a 5 - year period at 5% compounded continuously. Find (A) the present value, and (B) the accumulated amount of money flow at t=5

Answer #1

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The function f(x) = 900 represents the rate of flow of money in
dollars per year. Assume a 5-year period at 5% compounded
continuously. Find the present value at t = 5.

The function F(X)= 700e^0.03x represents the rate of flow of
money in dollars per year. Assume a 10 year period at 5 percent
compounded continuously. A. Find the present value B. the
accumulated amount of money flow at t=10?

1. An investment is projected to generate income at the rate of
R(t)=20,000 dollars per year for the next 4 years. If the income
stream is invested in a bank that pays interest at the rate of 5%
per year compounded continuously, find the total accumulated value
of this income stream at the end of 4 years.
2. Find the average value of the function f(x)=∜(5x+1) over the
interval [0,3].

The rate of a continuous money flow starts at $800 and increases
exponentially at 3% per year for 5 years. Find the present value
and final amount if interest earned is 4% compounded
continuously.
a) The present value is?
b) The final amount is?
(Do not round until the final answer. Then round to the nearest
cent as needed.)

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 accumulated present value of an investment over a 8
year period if there is a continuous money flow of $12,000 per year
and the interest rate is 1.6% compounded continuously.

Find the accumulated present value of an investment over a 6
year period if there is a continuous money flow of $9,000 per year
and the interest rate is 1.9% compounded continuously.

A young person with no initial capital invests k
dollars per year at an annual rate of return r. Assume
that investments are made continuously and that the return is
compounded continuously.
(a) Determine the sum S(t) accumulated at any time
t.
(b) If r = 6.0%, determine k so that $1
million will be available for retirement in 43 years.
(c) If k=2500/year, determine the return rate r that
must be obtained to have $1 million available in 43...

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

Construct a cash flow diagram that represents the amount of
money that will be accumulated in 7 years from an initial
investment of $20,000 now and $3,500 per year for 7 years at an
interest rate of 8% per year. And calculate what the final amount
after the 7 years will be.

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