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Elena L [17]
2 years ago
5

Matt inherited as a trust a fifteen-year annuity-immediate with annual payments. He has been told that the annuity payments earn

compound interest at a level rate and that at the end of fifteen years, their accumulated value will be $37,804.39. He has further been assured that figured at this same rate of interest, the value of his inheritance was $15,077.10. The trust executor will not reveal the amount of the annual payments. Determine this amount and also the annual effective interest rate earned by the annuity payments.
Business
1 answer:
Pavel [41]2 years ago
6 0

Answer:

effective annual interest rate = 6.32%

annual payment = $1,585

Explanation:

I believe that this is an ordinary annuity, so we can use the future and present value of an ordinary annuity formula:

FV = annual payment x FV annuity factor, so annual payment = FV / FV annuity factor

PV = annual payment x PV annuity factor, so annual payment = PV / PV annuity factor

we can equal both equations:

PV / PV annuity factor = FV / FV annuity factor

FV / PV = FV annuity factor / PV annuity factor

$37,804.39 / $15,077.10 = FV annuity factor / PV annuity factor

2.5074 = FV annuity factor / PV annuity factor

the easiest way to solve this is to use an annuity table since we already know that there are 15 periods (I used an excel spreadsheet):

%,15 periods      FV annuity factor     PV annuity factor        FV/PV

1                                 16.097                   13.865                      1.1609

2                                17.293                   12.849                      1.34586

3                                18.599                    11.938                      1.55797

4                               20.024                     11.118                       1.80104

5                                21.579                   10.380                      2.07890

<u>6                               23.276                   9.7122                       2.3966</u>

<u>7                                25.129                   9.1079                       2.7590</u>

8                                27.152                   8.5595                       3.1721

9                                29.361                   8.0607                      3.6425

10                               31.772                   7.6061                         4.4112

The interest rate must be between 6 and 7%:

%,15 periods      FV annuity factor     PV annuity factor        FV/PV

6                               23.276                   9.7122                       2.3966

6.1                             23.45404              9.6461                       2.43145

6.2                            23.63369              9.5858                      2.46549

6.3                            23.81491               9.52467                     2.50034

6.31                           23.83312               9.51851                     2.50387

<u>6.32                          23.85135               9.51236                     2.5074</u>

6.4                            23.99773              9.46337                     2.53585

effective interest rate = 6.32% per year

annual payment = $37,804.39 / 23.85135 = $1,585

           

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2 years ago
revorrow Corporation manufactures and sells a single product. The company uses units as the measure of activity in its budgets a
nlexa [21]

Answer:

$9,906 F

Explanation:

Calculation as follows:

Budget Income Statement

<u>Particular</u>                                                       $

Revenue (28.4 x 7,000)                          198,800

Direct Labor (2.8 x 7,000)                       (19,600)

Direct Material (10.7 x 7,000)                  (74,900)

Manufacturing Overheads

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Selling and administrative Expenses

(23,600 + [0.3 x 7,000] )                           (25,700)

Net Operating Income                               30,100

Actual Income Statement

<u>Particular</u>                                                       $

Revenue                                                   205,320

Direct Labor                                             (18,974)

Direct Material                                         (72,252)

Manufacturing Overheads                      (48,320)

Selling and administrative Expenses      (25,768)

Net Operating Income                             40,006

Activity variance for net operating income = Net operating income actual - Net operating income budgeted

Activity variance for net operating income = 40,006 - 30,100

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8 0
3 years ago
Sarah is a 50 percent partner in the SF Partnership and has an outside basis of $56,000 at the end of the year prior to any dist
Vikentia [17]

Answer:

A. $0 gain, $36,000 basis

Explanation:

In the distribution, from the information given, Sarah does not recognize any gain or loss.

However, given that

She had $56000 basis at end of year prior to distribution.

Then receives $20000 from distribution after reallocating her basis in SF to cash in amount equal to distribution

Therefore,

Her basis left = 56000 - 20000

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3 0
3 years ago
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2 years ago
Data concerning Farm Corporation's single product appear below: Selling price per unit $ 320.00 Variable expense per unit $ 76.8
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Answer:

$224,000

Explanation:

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= $320 - $76.8

= $243.2

Contribution margin ratio = Contribution margin / Sales

= $243.2 / $320

= $0.76 × 100

= 76%

Break even point = Fixed cost / Contribution margin ratio

= $170,240 / 76%

= $224,000

7 0
3 years ago
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