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babymother [125]
2 years ago
5

Calculate the annual cash flows (annuity payments) from a fixed-payment annuity if the present value of the 15-year annuity is $

750,000 and the annuity earns a guaranteed annual return of 6.85 percent. The payments are to begin at the end of the current year. Calculate the annual cash flows (annuity payments) from a fixed-payment annuity if the present value of the 15-year annuity is $750,000 and the annuity earns a guaranteed annual return of 6.85%. The payments are to begin at the end of five years. What is the amount of the annuity purchase required if you wish to receive a fixed payment of $100,000 for 25 years
Business
1 answer:
hram777 [196]2 years ago
8 0

Answer:

Calculate the annual cash flows (annuity payments) from a fixed-payment annuity if the present value of the 15-year annuity is $750,000 and the annuity earns a guaranteed annual return of 6.85%. The payments are to begin at the end of five years.

  • $81,567.49

What is the amount of the annuity purchase required if you wish to receive a fixed payment of $100,000 for 25 years

  • $1,181,276

Explanation:

present value of the ordinary annuity = $750,000

n = 15

interest rate = 6.85%

in order to calculate the annuity payment, we can use the formula for the present value of an annuity:

PV = annuity payment x annuity factor

annuity payment = PV / annuity factor

  • PV = $750,000
  • annuity factor 6.85%, 15 periods = 9.19484

annuity payment = $750,000 / 9.19484 = $81,567.49

since 6.85% is not a full number, it is hard to find annuity tables that contain it, but we can always search for annuity table calculators that can help us determine the annuity factor.

for the second question, we need to determine the PV of the ordinary annuity

PV = annuity payment x annuity factor

  • annuity payment = $100,000
  • annuity factor 6.85%, 25 periods = 11.81276

PV = $100,000 x 11.81276 = $1,181,276

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Suppose that output (Y ) in an economy is given by the following aggregate production function: Yt = Kt + Nt where Kt is capital
shusha [124]

Answer:

Check the explanation

Explanation:

Yt = Kt + Nt

Taking output per worker, we divide by Nt

Yt/Nt = Kt/Nt + 1

yt = kt + 1

where yt is output per worker and kt is capital per worker.

a) With population being constant, savings rate s and depreciation rate δ.

ΔKt = It - δKt

dividing by Nt, we get

ΔKt/Nt = It/Nt - δKt/Nt ..... [1]

for kt = Kt/Nt, taking derivative

d(kt)/dt = d(Kt/Nt)/dt ... since Nt is a constant, we have

d(kt)/dt = d(Kt/Nt)/dt = (dKt/dt)/Nt = ΔKt/Nt = It/Nt - δKt/Nt = it - δkt

thus, Capital accumulation Δkt = i – δkt

In steady state, Δkt = 0

That is I – δkt = 0

S = I means that I = s.yt

Thus, s.yt – δkt = 0

Then kt* = s/δ(yt) = s(kt+1)/(δ )

kt*= skt/(δ) + s/(δ)

kt* - skt*/(δ) = s/(δ)

kt*(1- s/(δ) = s/(δ)

kt*((δ - s)/(δ) = s/(δ)

kt*(δ-s)) = s

kt* = s/(δ -s)

capital per worker is given by kt*

b) with population growth rate of n,

d(kt)/dt = d(Kt/Nt)/dt =

= \frac{\frac{dKt}{dt}Nt - \frac{dNt}{dt}Kt}{N^{2}t}

= \frac{dKt/dt}{Nt} - \frac{dNt/dt}{Nt}.\frac{Kt}{Nt}

= ΔKt/Nt - n.kt

because (dNt/dt)/Nt = growth rate of population = n and Kt/Nt = kt (capital per worker)

so, d(kt)/dt = ΔKt/Nt - n.kt

Δkt = ΔKt/Nt - n.kt = It/Nt - δKt/Nt - n.kt ......(from [1])

Δkt = it - δkt - n.kt

at steady state Δkt = it - δkt - n.kt = 0

s.yt - (δ + n)kt = 0........... since it = s.yt

kt* = s.yt/(δ + n) =s(kt+1)/(δ + n)

kt*= skt/(δ + n) + s/(δ + n)

kt* - skt*/(δ + n) = s/(δ + n)

kt*(1- s/(δ + n)) = s/(δ + n)

kt*((δ + n - s)/(δ + n)) = s/(δ + n)

kt*(δ + n -s)) = s

kt* = s/(δ + n -s)

.... is the steady state level of capital per worker with population growth rate of n.

3. a) capital per worker. in steady state Δkt = 0 therefore, growth rate of kt is zero

b) output per worker, yt = kt + 1

g(yt) = g(kt) = 0

since capital per worker is not growing, output per worker also does not grow.

c)capital.

kt* = s/(δ + n -s)

Kt*/Nt = s/(δ + n -s)

Kt* = sNt/(δ + n -s)

taking derivative with respect to t.

d(Kt*)/dt = s/(δ + n -s). dNt/dt

(dNt/dt)/N =n (population growth rate)

so dNt/dt = n.Nt

d(Kt*)/dt = s/(δ + n -s).n.Nt

dividing by Kt*

(d(Kt*)/dt)/Kt* = s/(δ + n -s).n.Nt/Kt* = sn/(δ + n -s). (Nt/Kt)

\frac{sn}{\delta +n-s}.\frac{Nt}{Kt}

using K/N = k

\frac{s}{\delta +n-s}.\frac{n}{kt}

plugging the value of kt*

\frac{sn}{\delta +n-s}.\frac{(\delta + n -s)}{s}

n

thus, Capital K grows at rate n

d) Yt = Kt + Nt

dYt/dt = dKt/dt + dNt/dt = s/(δ + n -s).n.Nt + n.Nt

using d(Kt*)/dt = s/(δ + n -s).n.Nt from previous part and that (dNt/dt)/N =n

dYt/dt = n.Nt(s/(δ + n -s) + 1) = n.Nt(s+ δ + n -s)/(δ + n -s) = n.Nt((δ + n)/(δ + n -s)

dYt/dt = n.Nt((δ + n)/(δ + n -s)

dividing by Yt

g(Yt) = n.(δ + n)/(δ + n -s).Nt/Yt

since Yt/Nt = yt

g(Yt) = n.(δ + n)/(δ + n -s) (1/yt)

at kt* = s/(δ + n -s), yt* = kt* + 1

so yt* = s/(δ + n -s) + 1 = (s + δ + n -s)/(δ + n -s) = (δ + n)/(δ + n -s)

thus, g(Yt) = n.(δ + n)/(δ + n -s) (1/yt) =  n.(δ + n)/(δ + n -s) ((δ + n -s)/(δ + n)) = n

therefore, in steady state Yt grows at rate n.

5 0
3 years ago
A firm achieves differentiation parity ideally when
Alina [70]
A firm achieves differentiation parity ideally when it sells its products or services at a higher price than its competitors.  

The idea of parity is that a company sells its products at a higher cost than competitors even though the product or service isn't unique. Differentiation is when one companies products compete and are better than another with the same product. 
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2 years ago
On June 1, Norma Company signed a 12-month lease for warehouse space. The lease requires monthly rent of $550, with 4 months pai
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Answer:

Balance = $1,650

Explanation:

As Norma company has paid 4 months rent in advance, therefore at the end of June, norma company will record its 1-month expense as follows

Adjusting entry at the end of June would be

                             DEBIT       CREDIT

Entry

Rent Expense     $550

Prepaid Rent                         $550

The balance on Norma's prepaid expense would be

Prepaid Rent  = $2200

Rent Expense = ($550)

Balance = $1,650

7 0
3 years ago
Suppose a society begins by producing 3 units of X and 4 units of Y and then alters production to 4 units of X and 4 units of Y.
melisa1 [442]

Answer:

This situation means that resources were not being efficiently used.

If society managed to produce 1 more unit of X with the same resources and technology, this means that some resources were idle in the past, which causes inefficiency.

This also means that the combination 3 units of X and 4 units of Y is a point inside the PPF. However, we do not know if the combination 4 units of X and 4 units of Y is a point inside the PPF, or on the PPF, because there could be some other combination that could be even more efficient (for example 5 units of both X and Y with the same resources and technology).

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3 years ago
Warner Corp. sells goods on account for $10,000 on April 2. On April 20, the customer returns $3,000 of the merchandise. The cus
Studentka2010 [4]

Explanation:

The journal entry are as follows

On April 20

Sales returns A/c Dr $3,000

       To Account receivable A/c $3,000

(Being the sales returned of goods is recorded)

While recording this given transaction, we debited the sales return account and credited the account receivable account so that the proper posting could be done

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