Question

In: Economics

) The force of interest is given by: d(t)= 0.08−0.001t 0≤t <3 0.025t −0.04 3≤t <5...

) The force of interest is given by: d(t)= 0.08−0.001t 0≤t <3 0.025t −0.04 3≤t <5 0.03 5≤t ⎧ ⎨ ⎪ ⎩ ⎪ i) Calculate the present value at time 2 of a payment of Ksh 1,000,000 at time 10. ii) Calculate the annual effective rate of interest from time 2 to time 10 equivalent to the force of interest function in (i) above.

Expert Solution

First lets see what force of interest is.

The “force of interest” is that interest rate that compounds continuously, rather than compounding after a fixed time period (such as compounding every six months).

Now, we know that the Future value of a PV at an interest rate compounding continuously (force of interest) i is given by

FV=PVeⁿⁱ,

where PV is the present value, e is exponential, n is number of years and i is the force of interest.

It is given to us that force of interest is

0.08 − 0.001t, when 0 ≤ t < 3

0.025t − 0.04, when 3 ≤ t < 5

0.03, when t ≥5

Using this and the above formula for present value, we get

Present Value of a payment at time 2 of 1000000 at time 10 is

1000000*exp( -[0.2355 - 0.158])*exp ( -[0.1125 + 0.0075])*exp ( -[0.3 - 0.15])

= 1000000*exp(-0.3475) = 706,452.

B. Lets say that the annual effective rate of interest is i , then

706452(1 + i)⁸ = 1000000

⇒ i = 4.44%

Rahul Sunny answered 1 year ago

The force of interest varies as a linear function from t = 0 until t =...

The force of interest varies as a linear function from t = 0 until t = 5 and as a quadratic function From t = 5 until t =10 (t in years) and is continuous at all time points. Suppose the force of interest is 2% p.a. at t = 0, 4.5% p.a. at t =5, 8% p.a. at t = 8 and 10% p.a. at t = 10. a) Determine the functional form of the force of interest over...

Solve the following IVP specifically using the Laplace transform method (d^3)x/d(t^3)+x=e^(-t)u(t) f(0)=0 f'(0)=0 f''(0)=0...

Solve the following IVP specifically using the Laplace transform method (d^3)x/d(t^3)+x=e^(-t)u(t) f(0)=0 f'(0)=0 f''(0)=0 where u(t) is the Heaviside step function

Given the two lines (x, y, z) = (4, -3, 5) + t(2, 0, -3) (x,...

Given the two lines (x, y, z) = (4, -3, 5) + t(2, 0, -3) (x, y, z) = (4, -3, 5) + s(5, 1, -1) a) determine a vector equation for the plane that combines the two lines b) parametric equations of the plane that contains the two lines c) Cartesian equation of the plane that contains the two lines

Which project should D&A should pick? Project A: t 0 1 2 3 4 5 6...

Which project should D&A should pick? Project A: t 0 1 2 3 4 5 6 7 8 9 10 CF 10,000 -55,000 155,000 125,000 119,000 113,500 201,500 123,000 -119,000 54,000 Project B: t 0 1 2 3 4 5 6 7 8 9 10 CF 95,000 112,000 155,000 -125,000 119,000 -153,000 255,000 -113,000 139,000 39,000 The cost of capital (discount rate) for both projects is 7.89% /year. Based on the given information, please calculate the present value of the...

A thumbs up will be given: Table 1 t A B C D 0 (14,900,000)...

A thumbs up will be given: Table 1 t A B C D 0 (14,900,000) (17,900,000) (16,600,000) (19,700,000) 1 4,980,000 5,990,000 3,850,000 6,400,000 2 4,980,000 6,210,000 4,990,000 5,880,000 3 4,510,000 6,250,000 6,860,000 6,800,000 4 4,510,000 4,700,000 4,990,000 6,650,000 Risk High Average Low Average Table 1 shows the expected after-tax operating cash flows for each project. All projects are expected to...

The annual force of interest credited to a savings account is given by δt=t/(10+t2).Find the present...

The annual force of interest credited to a savings account is given by δt=t/(10+t2).Find the present value of $7,000 at time 3.

Given the following data (2, 5, 1, 0, 5, 0, 7, 2, 3) Calculate the 3rd...

Given the following data (2, 5, 1, 0, 5, 0, 7, 2, 3) Calculate the 3rd quartile from your "data". What's the probability that a randomly selected number from your data is even? Consider the events A = "a randomly selected number from your data is even" and B = "a randomly selected number from your data is above the 3rd quartile". Are these events disjoint, independent, neither, or both? Show your work.

A particle is moving according to the given data v(t)=t^2 - sqrt(t), x(0) = 0, 0...

A particle is moving according to the given data v(t)=t^2 - sqrt(t), x(0) = 0, 0 ≤ t ≤ 4. • Find x(t), the position of the particle at time t. • For what values of t is the particle moving to the left? To the right? • Find the displacement of the particle. • Find the total distance covered by the particle.

Given X′=AX with X(t)=[x(t)y(t)], A=[23−4012−21] and X(0)=[3−4]

Given X′=AX with X(t)=[x(t)y(t)], A=[23−4012−21] and X(0)=[3−4]. (a) Write the eigenvalues and eigenvectors of A λ1= , V1= ⎡⎣⎢⎢ ⎤⎦⎥⎥ , and λ2= , V2= ⎡⎣⎢⎢ ⎤⎦⎥⎥ (b) Write the solution of the initial-value problem in terms of x(t),y(t) x(t)= y(t)=

you put aside 100,000 in year t=0 and let it grow at 5.8% interest for 5...

you put aside 100,000 in year t=0 and let it grow at 5.8% interest for 5 years. exactly one year after that you start to withdraw your money for 3 years in equal amounts until it is exhausted. How much can you withdraw per year?