ssume you lend $10.000 for a five (5) year period. The current the real rate at the time you lend the money is 2.3%. You charge no
risk premium on the loan.
At the end of the 5-years loan period you receive back your $10,000 and then decide to determine your rate of return. You collect the following information for your calculation.

1)Using the Fisher Equation, what is your expected required rate of return on the loan? Show clearly all work, carrying all calculations out to four (4) decimal places. Highlight in bold your answer.

2) Using the Fisher Equation, what is your realized required rate of return on the loan? Show clearly all work, carrying all calculations out to four (4) decimal places. Highlight in bold your answer.

Thank you.

Please justify below questions (its a topology question) with valid arguments:

1. Show that an infinite set is not finite.

2. Is there an infinite set which is not countably in finite?

Thanks in advance.

List examples of equations similar to the Pell's equation, ie. any  Diophantine equation other then Pell's.

Find a general solution of the following equations:

A. y′′′ +6y′′ +11y′ +6y = −e^-t

B. y′′′ + y′ = t.

V and W are finite dimensional inner product spaces,T:V→W is a linear map, and∗represents the adjoint.

1A: Let n be a positive integer, and suppose that T is defined on C^n (with the usual inner product) by T(z1,z2,...,zn) = (0,z1,z2,...,zn−1). Give a formula for T*.

1B: Show that λ is an eigenvalue of T if and only if λ is an eigenvalue of T*.

Use stars and bars to solve each counting problem. You may leave your answers as binomial coefficients.

(a) How many collections of 6 (not necessarily distinct) coins can be made from an infinite supply of pennies, nickels, dimes, and quarters?

(b) A social security number is a sequence of 9 digits. How many social security numbers are there n1n2n3 . . . n9 such that ni ≤ ni+1 for i = 1 to 8? For example, 024455888 would count but 254180419 would not count

Find the intersection of the line passing through P=(21,21) and Q(−63,168) and the line passing through points R(21,0) and S(0,21) using vectors.

For each of the following simplicial complexes ,X = {[a], [b], [c], [d], [a, b], [c, d]}, and X = {[a], [b], [c], [d], [e], [a, b], [b, c], [c, d], [a, d], [a, c], [a, e], [b, e], [a, b, c]},give a basis for each non-zero Hj(X).

Find the distance from

(2, −7, 7)

to each of the following.

(a) the xy-plane

(b) the yz-plane

(c) the xz-plane

(d) the x-axis

(e) the y-axis

(f) the z-axis

195 dots are placed in a square that is 4 x 4 units.

This configuration creates an issue where at least two points need to be very close to one another, no farther than a distance of D. What is the minimum distance D? (Hint: Consider using pigeonhole principle to solve min distance)

3. A small fire is sighted from ranger stations A and B. The bearing of the fire from station A is N35E, and the bearing of the fire from station B is N49W. Station A is 1.3 miles due west of station B.

a) How far is the fire from each station?

b) At fire station C, which is 1.5 miles from A, there is a helicopter that can be used to drop water on the fire. If the bearing of C from A is S42E, find the distance from C to the fire, and find the bearing of the fire from

C. Note: A neat labeled diagram is required.

8. Determine the unique solution of the given initial value problem that is valid in any interval not including the singular point.

              4x² y’’ + 8xy’ + 17y = 0;             y(1) = 2, y’ (1) = 2(3^1/2 )− 1

please show all steps

QUESTION: In each part, find a formula for a vector field consistent with the description. Provide at least one numeric example showing the consistency of the formula and the description (an example follows the descriptions).

1.All vectors are parallel to the x-axis and all vectors on a vertical line have the same magnitude.

2.All vectors point toward the origin and have constant length.

3.All vectors are of unit length and are orthogonal to the position vector at that point.

A three-phase 60-Hz transmission line is energized with 420 kV at the sending end. This line is lossless and 400 km long with ? = 0.001265 rad/km and ?? = 260 Ω. a) Suppose a three-phase short-circuit occurs at the receiving end. Determine the receiving end current and the sending end current. b) Determine the reactance and MVar of a shunt reactor to be installed at the load bus to limit the no-load receiving-end voltage to 440 kV. c) When the line delivers 800 MVA at 0.8 lagging power factor, a shunt capacitor bank is installed at the receiving end to improve the line performance. Determine the total Mvar and the capacitance of the Δ-connected capacitor bank to keep the receiving-end voltage at 400 kV when the sending-end voltage is 420 kV.