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svetoff [14.1K]
3 years ago
8

A woman worked for 30 years before retiring. At the end of the first year of employment she deposited 5000 into an account for h

er retirement. At the end of each subsequent year of employment, she deposited 3% more than the prior year. The woman made a total of 30 deposits. She will withdraw 50,000 at the beginning of the first year of retirement and will make annual withdrawals at the beginning of each subsequent year for a total of 30 withdrawals. Each of these subsequent withdrawals will be 3% more than the prior year. The final withdrawal depletes the account. The account earns a constant annual effective interest rate. Calculate the account balance after the final deposit and before the first withdrawal.
Business
1 answer:
Mrrafil [7]3 years ago
8 0

Answer:

$797,837

Explanation:

the first withdrawal is $50,000

the second is $51,500

and so on...

the formula that used to solve the interest rate earned by the annuity is:

$50,000 x {[(1 + i)³⁰ - (1 + 3%)³⁰] / [(1 + i)³⁰ x (i - 3%)]} x (1 + i) = $5,000 x {[(1 + i)³⁰ - (1 + 3%)³⁰] / (i - 3%)}

we start to simplify the equation by cancelling  {[(1 + i)³⁰ - (1 + 3%)³⁰] / (i - 3%)}

[$50,000 x (1 + i)] / (1 + i)³⁰ = $5,000

now we cancel $5,000 on each side:

[10 x (1 + i)] / (1 + i)³⁰ = 1

now lets take away (1 + i):

10 / (1 + i)²⁹ = 1

things get a little bit more simple now:

10 = (1 + i)²⁹

²⁹√10 = ²⁹√(1 + i)²⁹

1.082636734 = 1 + i

i = 1.082636734 - 1 = 0.082636734 = 8.2636734%

now we replace i in any equation:

= $50,000 x {[(1 + 0.082636734)³⁰ - 1.03³⁰] / [(1 + 0.082636734)³⁰ x (0.082636734 - 0.03)]} x (1 + 0.082636734)

= $50,000 x  {[10.82636738 - 2.427262471] / [10.82636738 x 0.052636734]} x (1 + 0.082636734)

= $50,000 x  {8.399104909 / 0.56986462} x (1.082636734)

= $50,000 x 14.73877236 x 1.082636734

= $797,837

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6 0
3 years ago
Burruss Company developed a static budget at the beginning of the company's accounting period based on an expected volume of 8,0
katrin2010 [14]

Answer:

The flexible budget would show fixed costs of $16,000

Explanation:

Meaning of Fixed cost: The fixed cost is that cost which is not have any impact on production level. It means that if the production level is increase or decrease, the fixed cost remain constant.

In the question the following information is given ,

Expected volume - 8,000 units

Per unit Revenue -  $ 4.00

Variable costs [per unit - 1.50

Contribution margin per unit -  $ 2.50

Fixed costs per unit - 2.00

Net income per unit -  $ 0.50

Actual production - 10,000 units

For computing the fixed cost under flexible budget for actual production which produces 10,000 units. The fixed cost remain same.

So, For 8000 units, the fixed cost = Units × Fixed cost per unit

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                                                        =$16,000

Hence, For 10,000 units, the fixed cost would be $16,000 as fixed cost remain same.

Thus, the flexible budget would show fixed costs of $16,000

4 0
3 years ago
Cholula hot sauce, a mexican made chili-based sauce brand, is introducing a new hot sauce flavor and wants to use its owners’ un
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6 0
2 years ago
Levelor Company's flexible budget shows $10,710 of overhead at 75% of capacity, which was the operating level achieved during Ma
Salsk061 [2.6K]

Answer:

The correct answer is $473 (Unfavorable).

Explanation:

According to the scenario, the given data are as follows:

Actual overhead = $11,183

Budgeted Overhead = $10,710

So, we can calculate the controllable variance by using following formula:

Controllable variance  = Actual overhead - Budgeted overhead

By putting the value, we get

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3 0
3 years ago
You have just won the lottery and will receive $460,000 in one year. You will receive payments for 27 years, and the payments wi
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Answer:

The present Value of my winnings = $4,578,716.35

Explanation:

An annuity is a series od annual cash outflows or inflows which payable or receivable for a certain number of periods. If the annual cash flow is expected  to increase by a certain percentage yearly, it is called a growing annuity.

To work out the the present value of a growing annuity,

we the formula:

PV = A/(r-g) ×  (1-  (1+g/1+r)^n)

I will break out the formula into two parts to make the workings very clear to follow. So applying this formula, we can work out the present value of the growing annuity (winnings) as follows.

A/(r-g)

= 460,000/(12%-3%)

= $5,111,111.11

(1-  (1+g/1+r)^n

1 - (1+3%)/(1+12%)^(27)

=0.8958

PV = A/(r-g) ×  (1-  (1+g/1+r)^n)

$5,111,111.11 × $0.8958

= $4,578,716.35

The present Value of my winnings = $4,578,716.35

5 0
3 years ago
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