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Ronch [10]
3 years ago
12

A deposit of $5000 is made to a bank account paying 1.5% annual interest, compounded continuously. (a) Write the differential eq

uation for the balance in the account, B, as a function of time, t, in years. (b) Solve the differential equation. (c) How much money is in the account in 10 years?
Business
1 answer:
seraphim [82]3 years ago
7 0

Answer:

Please find the detailed answer as follows:

Explanation:

A. Step 1. The differential equation is

dB / dt = 0.015B - 5000

 

Step 2.   now we must integrate it to find it ias a function of time

dB /0.015B - 500 = dt

 

Step 3. integrate

=> ln ( 0.015 B - 5000) = 0.015t + 0.015c

=> 0.015B - 5000 = e^0.015t .e^0.015c

here .e^0.015c is constant let it be Bo

b. =>B = 1/0.015 [ Bo e^0.015t + 5000 ]

at t = 0 , B = 5000  

=> 5000 x 0.015 = Bo => B o = 75

c . B = 1/0.015 [ 75 e^0.015t + 5000 ]

put t = 10  

=> B = $ 339142.50

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Nataly_w [17]

Answer:

1. Able must pay Regal Corporation $599,400 on September 1, 2019, when the note matures.

2. The amount of Interest Able will recognize on this Notes Payable is 39,600

3. The total cash (including interest) paid for the building purchased by Able is $1,179,400

4. Payroll related expense does not come into picture in this question. So it is not answered.

Explanation:

1. According to the given data we have the following:

Rate of Interest = 11%

Therefore:      

Year                      Amount Interest      

September 1, 2018       $540,000      

December 31, 2018            $19,800      

September 1, 2019                     $39,600      

Total                      $540,000     $59,400

Therefore, Total Payable=Notes payable+Interest 540000      Total Payable= $540,000+$59,400

Total Payable=$599,400

Able must pay Regal Corporation $599,400 on September 1, 2019, when the note matures.

2. The amount of Interest Able will recognize on this Notes Payable is 39,600

3. To calculate The total cash paid for building purchased by Able including interest we have to make the following calculation:

Total cash paid for purchase of building=Cash paid at the time of purchase of building+Notes payable+Interest

Total cash paid for purchase of building=$580,000+$540,000+$59,400

Total cash paid for purchase of building=$1,179,400

The total cash (including interest) paid for the building purchased by Able is $1,179,400

4. Payroll related expense does not come into picture in this question. So it is not answered.

6 0
3 years ago
What does a bdc invest in? a publicly-held small-cap companies b publicly-held mid-cap companies c privately-held small-cap and
Anna007 [38]

Business development companies are known as BDCs. It is a 1940 Act-registered investment company that trades and is listed just like any other stock.

<h3>What is BDC?</h3>

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A BDC often invests in private enterprises using equity securities or debt (loans). It looks for ways to produce current income and/or capital gains that are tax-efficient. BDCs are regulated in a similar way to mutual funds, but they often use leverage to produce excess returns.

A BDC is a closed-end fund that must allocate at least 70% of its assets to long-term debt and/or equity investments in privately held or thinly traded public companies in order to generate current income and/or capital gains.

Business development companies are known as BDCs. It is a 1940 Act-registered investment company that trades and is listed just like any other stock. It makes "private equity" investments in privately held start-up companies as well as mid-sized businesses rather than making investments in securities.

Hence, The correct option is  C.

What does a BDC invest in?

A. Publicly-held small-cap companies

B. Publicly-held mid-cap companies

C. Privately-held small-cap and mid-cap companies

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8 0
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lyudmila [28]

Answer:

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Each time you can climb 1 or 2 steps to the top (n steps)

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Number of ways climbing 2 steps to the top = n combination 2 = n!/(n-2)!2! = n(n-1)(n-2)!/2(n-2)! = (n^2 - n)/2

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The correct answer is C.

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So the completed balanced equation is:
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I hope this helps! :)
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6 0
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