Given:
Now,
S0 = a0 + [a1/(1 +r)] + [a2/(1 +r)2] + …….. + [an/(1 +r)n]
= a0 + [a0(1 +g)/(1 +r)] + [a0(1 +g)2/(1 +r)2] + …….. + [a0(1 +g)n/(1 +r)n]
= a0 [1 + (1 +g)/(1 +r) + (1 +g)2/(1 +r)2 + …….. + (1 +g)n/(1 +r)n]
=
[ Since, sum of finite GP series: a(1 - rn/(1 - r)]
On simplifying, we get:
S0 = a0[(1 – r) – (1 + g)n(1 + r)1-n]/(r – g)
Problem 1 Suppose there is a series of cashflows that lasts n + 1 peri- ods, {at}t, 0 < t <n, and that is growing...
Problem 1 Suppose there is a series of cashflows that lasts n1 peri ods, {at}, 0 < t < n, and that is growing at constant rate g, (1 g)ao, Vt. The discount rate is fixed at r and assume g < r. Find an expression for the discounted present value of the cashflows at time 0. Formally, find an expression for S i.e. at a1 = aot 1+r an (1+r)"
Problem 1 Suppose there is a
series of cashflows that lasts n + 1 periods, {at}t , 0 ≤ t ≤ n,
and that is growing at constant rate g, i.e. at = (1 + g) ta0, ∀t.
The discount rate is fixed at r and assume g < r. Find an
expression for the discounted present value of the cashflows at
time 0. Formally, find an expression for S = a0 + a1 1+r + ... + an
(1+r)...
Problem 1 Suppose there is a series of cashflows that lasts n + 1 pery- ods, {at}, 0 <t<n, and that is growing at constant rate 9, i.e. a4 = (1 + g)'ao, Vt. The discount rate is fixed at r and assume g <r. Find an expression for the discounted present value of the cashflows at time 0. Formally, find an expression for S = do + 12 + ... + (147)
8.3 Consider the periodic wave equation for t E R and x e T. Suppose the initial conditions are or (0, x) h(x), for g є Cm +1 (T) and h є Cm(T), for m E N. 152 8 Fourier Series (a) Assuming that u(t, x) can be represented as a Fourier series u(t, x)- av(l)ekx, kEZ (8.48) find an expression for ak() in terms of the Fourier coefficients of g and h.
Find the sum of the series
Problem #13 an IS Sn4n - 1 n-1 Suppose that the nth partial sum of the series 5n+ 3 (a) Find a3 (b) Find n-1 Problem #13(a): 10/117 Problem #13(b): Your work has been saved! (Back to Admin Page) Submit Problem #13 for Grading Just Save
Suppose a population is growing according to the logistic formula N = 510/1+3e^-0.41t where t is measured in years. (a) Suppose that today there are 250 individuals in the population. Find a new logistic formula for the population using the same K and r values as the formula above but with initial value 250. (Round equation parameters to two decimal places.) (b) How long does it take the population to grow from 250 to 360 using the formula in part...
Problem 2 Statement: We know that the binomial series k k(k-1) k1 2)(k -n+1 n=0 converges for l < 1. (a) Use the binomial series to find the Taylor series for f(x)Va centered at z 16. What is the radius 16+ ( 16). of convergence R for your Taylor series? Hint:
Problem 2 Statement: We know that the binomial series k k(k-1) k1 2)(k -n+1 n=0 converges for l
Section 2.1 I. Suppose 2(t) if 4<t 5 otherwise Determine the absolute time duration of this signal and plot it. 2. Suppose rn]-1 if n 23 otherwise Classify this signal as left-sided, right-sided, two-sided, or time-limited and plot it. Section 2.2 3. Suppose r(t) is as given in Problem 1. Plot and give an expression for y(t) - (^ + ^t). Also determine the turn-on and turn-off times for y(t) 4. Suppose a[n] is as given in Problem 2. Plot...
1. PE ratios a.) Consider the following asset pricing equation D+P. 1+r Pi is the real price of one share of stock and Di is the real dividend payment per share at time t. The company pays out all profits in dividends and the real interest rate is constant. Show that if the company lasts forever, and if the real interest rate is constant, then t r b.) Suppose dividends grow indefinitely at rate g so D+1-D (1+8). Assume that...