An amortized loan requires 500 end of month payments of 1, 2, 3, 4, ..., 499, 500. The nominal interest rate is 6% convertible monthly. Find the outstanding balance of the loan immediately after the 5th payment.

(a) 30514.11 (b) 29342.46 (c) 29327.36 (d) 28619.77 (e) 31589.03

MATLAB question!

4. (a) Modify the code, to compute and plot the quantity E = 1/2mv^2 + 1/2ky^2 as a function of time. What do you observe? Is the energy conserved in this case?

(b) Show analytically that dE/dt < 0 for c > 0 while dE/dt > 0 for c < 0.

(c) Modify the code to plot v vs y (phase plot). Comment on the behavior of the curve in the context of the motion of the spring. Does the graph ever get close to the origin? Why or why not?

given code
---------------------------------------------------------------

clear all;   
m = 4; % mass [kg]
k = 9; % spring constant [N/m]
c = 4; % friction coefficient [Ns/m]
omega0 = sqrt(k/m); p = c/(2*m);
y0 =-0.8; v0 = 0.3; % initial conditions
[t,Y] = ode45(@f,[0,15],[y0,v0],[],omega0, p); % solve for 0<t<15
y = Y(:,1); v = Y(:,2); % retrieve y, v from Y
figure(1); plot(t,y,'ro-',t,v,'b+-');% time series for y and v
grid on; axis tight;
%---------------------------------------------------
function dYdt = f(t,Y,omega0,p); % function defining the DE
y = Y(1); v = Y(2);
dYdt=[ v ; -omega0^2*y-2*p*v]; % fill-in dv/dt
end

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(a) Find the exact length of the curve y = 1/6 (x² + 4)^(3/2) , 0 ≤ x ≤ 3. (b) Find the exact area of the surface obtained by rotating the curve in part (a) about the y-axis.

I got part a I NEED HELP on part b

Draw the VSEPR picture for (1) CO2, (2) CH2O, (3) CH4, (4). C2H6, and Identify the,

(A) electron pair geometry, (B) the molecular geometry and (C). the bond angles.

1. Consider a rolling two four-sided dice with faces 1, 2, 3 and 4.

(a) Obtain the pmf of X where X is the sum of the two resultant faces

         (b) Suppose the two die were rolled many times. Approximately, what would

would be the average of X?

(c) Calculate the standard deviation of X.

Consider the cash flow for projects A and B Year: 0, 1, 2, 3, 4, 5

Project A: ($1000), 100, 600, 700, 900, 300

Project B: ($1000), 900, 700, 500, 300, 300

The cost of capital for both projects is 10%

1. Find NPV, IRR and profitability index (PI) of projects A and B.

2. If projects A and B are mutually exclusive, which project would you select

3. Find the crossover rate for projects A and B

1.) Suppose you will go to graduate school for 2 years beginning in year 4. Tuition is $28,359 per year, due at the end of each school year. What is the Macaulay duration (in years) of your grad school tuitions? Assume a flat yield curve of 0.06. Assume annual compounding. In the above description, if you see a flat yield curve of 0.08 for example, then it means that the yield at all maturities is 8%.

2.) Suppose in the question above, the tuition obligations have a Macaulay duration of 5.06 in years, and that you wish to immunize against the tuition payments by buying a single issue of a zero coupon bond. What maturity zero coupon bond should you buy?

Assume annual compounding. Round your answer to 2 decimal places.

3.) Suppose in question 1, the tuition obligations have a Macaulay duration of 5.96 in years and a present value of 57,321. In order to immunize against the tuition payments by investing in some combination of two bonds with duration 2.83 and 8.61, what is the dollar amount that you should invest in the bond with duration 8.61?

Assume annual compounding. Round your answer to 2 decimal places.

There are two projects with the following cash flows.

Years: 0 1 2 3 4 5

Project 1: -210 125 125 175 175 -400

Project 2:  300 -95 -75 -125 -400 600

a. What are the NPVs of these two projects if market interest rate is 3%?

b. With the interest rate of 6%, please modified these two projects to let them have only one IRR for each one of them. (That means the sign of cash flows of each project only changes for one time.) And then, calculate the Modified IRRs.

c. With the interest rate of 6%, compute the discounted payback periods of both projects.

d. Please calculate the IRR of incremental cash flows based on two projects.

consider the following state vectors
|psi subscript 1> =3|+> + 4|->
|psi subscript 2> = |+> + 2i |->
|psi subscript 3> = 3|+> - e exp ipi\3 |->

Now , normalize each state vector

then , For each state vector calculate the probability that the spin components is up or down along each of the three cartesian axes . Use bra-ket notation for the entire calculation.