6. Two funds are started with equal deposits at time t = 0. Fund X is...
At time 0, $20,000 is deposited into Fund X, which accumulates at a varying force of interest of 0.09 -0.004t. At time 0, $15,000 is deposited into Fund Y which accumulates at an annual effective discount rate of 9% for the first 5 years, and a constant force of interest for the last five years. At time t = 10, Fund X and Fund Y's accumulated values are the same. What is the constant force of interest at which Fund...
Fundamentals of Financial Mathematics question:
QUESTION 7 On 01/01/1997, Kelly deposits X into a bank account. The account is credited with simple interest at the rate of 10% per year On the same date, Tara deposits X into a different bank account. The account is credited interest using a force of interest, for t being time in years since the investment is made where 2t (t+k) From the end of the 4th year until the end of the s"h year,...
1000 is invested at time t = 0. At any given time, the investor can transfer the funds from either of accounts X and Y . Additionally, Account X grows by a constant force of interest of 10%. Account Y grows by the force of interest δ(t) = t/(1 + t2) Find the maximum amount of the investor's account balance at time t = 12.
(20 points) Josh makes deposits of 1000 at time 0 and X at time 4. His balance grows at a force of interest dt = t- t> 0. The amount of interest earned from time 3 to time 6 is also X. Calculate X.
6. An investor deposits $2000 into a fund at time 0. Four months later when his balance has declined to $1900 he withdraws $300. After four more months his balance is $1800 and he deposits $500. At the end of a year his balance is 2400. a. Find this investor' s (dollar weighted) annual rate of return. (You can assume simple interest.) b. find the fund's annual (time weighted) rate of return. 6a. Current spot rates are si- 0.025, s2...
Allison throws a tennis ball at time t = 0 from a height h above the ground equal to her own height. We assume that the positive horizontal direction is the positive x-direction, and the positive vertical direction is the positive y-direction. The ball has a positive initial horizontal velocity vx, and no initial vertical velocity. At times t1 and t2, the ball bounces on the ground for the first, and second times respectively after being thrown. We assume that...
Consider an event with space-time coordinates (t=2.00s,x=2.50 x 108m)in an inertial frame of reference S. Let S' be a second inertial frame of reference moving, in the positive x direction, with speed 2.70 x 108m/s relative to frame S. Find the value of gamma that will be needed to transform coordinates between frames S and S'. Use c=3 x 108m/s for the speed of light in vacuum. Suppose that S and S' share the same origin; that is, at t...
1. Let {x, t,f 0) and {Yǐ.12 0) be independent Poisson processes,with rates λ and 2A, respectively. Obtain the conditionafdistributiono) Moreover, find EX Y X2t t given Yt-n, n = 1,2. 2, (a) Let T be an exponential random variable with parameter θ. For 12 0, compute (b) When Amelia walks from home to work, she has to cross the street at a certain point. Amelia needs a gap of a (units of time) in the traffic to cross the...
Problem 4 Let x(t) be a continuous time signal whose Fourier transform has the property that Xe(ja)0 for lal 2 2,000. A discrete time signal aIn]x(n(0.5x 10-3)) is obtained. For each of the following constra ints on Xa(e/n), the Fourier transform of xaln], determine the coresponding constraint on Xe(ja) a) X(en) is real b) The maximum value of X4 (ea) over all is 1 c) Xa(ea)= Xa(e/ a-)
Problem 4 Let x(t) be a continuous time signal whose Fourier transform...
A simple harmonic oscillator at the position x=0 generates a
wave on a string. The oscillator moves up and down at a frequency
of 40.0 Hz and with an amplitude of 3.00 cm. At time t =
0, the oscillator is passing through the origin and moving down.
The string has a linear mass density of 50.0 g/m and is stretched
with a tension of 5.00 N.
A simple harmonic oscillator at the position x = 0 generates a wave...