Question

a. If an account has an APR of 100 r % compounded continuously, its annual growth factor is

b. Based on your answer to part (a), the accounts t -year growth factor must then be

c.Based on your answers to parts (a) and (b), what is the account value after t years if P dollars is initially invested in the account?

d.Therefore, the function A that models the account's value after t years if interest is compounded continuously is (use the same parameter letters defined above):

Answer #1

Ans a. |

If APR =r=100% with continuous compounding, |

Annual Growth factor =e^100 |

Where e=2.7183 approx. |

Ans b. |

The Accounts t year growth factor will be =e^(rt) |

Where e=2.7183 approx. |

Ans c. |

if P dollars initially invested, maturity amount after |

t-years will be =P*e^(rt) |

Where e=2.7183 approx. |

Ans d. |

the function A that models the account's value |

after t years if interest is compounded continuously is |

A=P*e^(rt) |

Where e=2.7183 approx. |

P=Initial $ investment |

3. Matt invested $5,500 into an account earning 2.5% APR
compounded continuously. What will his balance be after seven
years?
4. How much money should be deposited in an account today that
earns 3.5% compounded monthly so that it will accumulate to $10,000
in 8 years?

Are
you invest in a bank account which pays 6% compounded continuously.
You withdraw money continuously at a rate of $4000 per month. Let B
be the balance in dollars and T be in time year in years. Suppose
you initially start with $3 million.
a)
set up a differential equation for the situation. Include the
initial condition. Do not solve.
b)
find the equilibrium for the differential equation. Is it stable or
unstable?

The future value that accrues when $700 is invested at 5%,
compounded continuously, is S(t) = 700e0.05t where t is the number
of years. (Round your answers to the nearest cent.) (a) At what
rate is the money in this account growing when t = 4? $ per year
(b) At what rate is it growing when t = 10? $ per year

When interest is compounded continuously, the amount of money
increases at a rate proportional to the amount S present
at time t, that is,
dS/dt =
rS,
where r is the annual rate of interest.
(a)
Find the amount of money accrued at the end of 8 years when
$5000 is deposited in a savings account drawing 5 3/4
% annual interest compounded continuously. (Round your answer to
the nearest cent.)
$
(b) this is the part I’m having the...

1)We invest $50 per month in an account that pays 3% interest
per year compounded continuously. How much is our account worth
after 7 years? Round your answer to the nearest penny.
2)We invest $50 per month in an account that pays 3% interest
per year compounded continuously. If we make these deposits for 7
years, what is the present value of this account? Round your answer
to the nearest penny.

When interest is compounded continuously, the amount of money
increases at a rate proportional to the amount S present
at time t, that is,
dS/dt =
rS,
where r is the annual rate of interest.
(a)
Find the amount of money accrued at the end of 8 years when
$5000 is deposited in a savings account drawing 5
3
4
% annual interest compounded continuously. (Round your answer to
the nearest cent.)
$
(b)
In how many years will the...

How
much needs to be deposited into an account that pays 4.05% APR
compounded in order for the account value to be worth $100,000
after 10 years
a)
Yearly?
b)
monlthly?
c)
weekly?
d)
daily?

1) When interest is compounded continuously, the amount of money
increases at a rate proportional to the amount S present
at time t, that is,
dS/dt =
rS, where r is the annual rate of
interest.
(a)Find the amount of money accrued at the end of 9 years when
$4000 is deposited in a savings account drawing 5 1/4 $ % annual
interest compounded continuously. (Round your answer to the nearest
cent.)
(b)In how many years will the initial sum...

1a)
Let S = $50, K = $55, r = 8% (continuously compounded), T =
0.25, and d = 0. Let u = 1.25, d = 0.7, and n = 1. What are D and B
for a European put?
Answers:
a.
D = –0.5055; B = 48.6981
b.
D = –0.6640; B = 34.3515
c.
D = –0.9695; B = 48.6535
d.
D = –0.7273; B = 44.5545
e.
D = –0.5607; B = 48.2080
1b) Let S =...

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].

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