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# Two unknowns

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Hello. Can anyone help me with this problem? I need to resolve but I can not at all. Please, I need the step-by-step resolution, or at least the beginning. I can not get out of the statement. Thanks.

6600+0,0075X = X * (1+y*(28/12))

Thanks.

Jan 14, 2018

#1
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What do you want to solve for? What do the instructions say?

Jan 14, 2018
#2
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It's a Financial Calculation problem.

A certain capital applied in simple interest at the annual rate during 27 months produced the accumulated capital of 6600 €. If the same capital was applied at the same rate but for 28 months, the cumulative capital reference would be increased by an amount corresponding to 0.75% of the initial capital. Calculate the starting capital and the annual rate to which it was applied.

I arrived at the initial formula, but then I do not know how to solve:

Equity = Initial Capital * (1 + rate * time), this is the calculation formula for accumulated capital.

6600 + 0,0075C0 = C0 * (1 + i * (28/12))

`Little remark: I am Portuguese. `
Guest Jan 14, 2018
edited by Guest  Jan 14, 2018
edited by Guest  Jan 14, 2018
#3
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OK, your problem is not stated very clearly! But, as far as I can understand you, this is what I think  your problem is:

If the initial Capital was C, then you have:

C x i% x 27 = 6,600..........................................(1)

C x i% x 28 = 6,600 + 0.0075C.........................(2), solve for i% and C

i =0.0075 pe month!!, and: 0.0075 x 12 x 100 =9% annual simple interest.

C=32,592.60 - Euros - The initial capital.

NOTE: I used SIMPLE INTEREST and not COMPOUND INTEREST, because your question says" applied 'simple interest'". Give us some feedback, so that we can help you solve the problem.

Jan 14, 2018
edited by Guest  Jan 14, 2018
edited by Guest  Jan 14, 2018
#4
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Here's my best guess, but I could easily be wrong.....

Let  c  be the starting capital,  and let  i  be the annual interest rate.

accumulated capital after  27  months   =   c(1 + i * 27/12)   =   6600

accumulated capital after  28  months   =   c(1 + i * 28/12)   =   6600 + 0.75% * c

Now we have two equations and two variables.

c(1 + i * 28/12)   =   c(1 + i * 27/12) + 0.75% * c         Divide through by  c .

1 + i * 28/12   =   1 + i * 27/12 + 0.75%                       Subtract  1  from both sides.

i * 28/12   =   i * 27/12 + 0.75%                                   Subtract  i * 27/12  from both sides.

i * 1/12   =   0.75%                                                      Multiply both sides by  12 .

i   =   9%

If I have interpreted the question correctly, this makes sense because it tells you that an additional month of interest adds 0.75% of the capital. That means that 0.75% is the annual rate / 12 . I might have not interepreted the question correctly.

Now....using this value of  i  , we can find  c .

c(1 + 9% * 27/12)   =   6600

c( 1.2025 )   =   6600                      Divide both sides of the equation by  1.2025 .

c   ≈   5488.57

Jan 14, 2018
#5
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Thank you very much for the help! That's it.

I'll enjoy it for a while, without wanting to abuse

- A capital of € 7000 was applied on a flat-rate basis at the half-yearly rate of 4% over a given period and produced an accumulated capital of more than € 1,400 to that which would be obtained if the period was reduced by half. Calculate the term of capital application.

Guest Jan 14, 2018
#6
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Okay, I'll give this one a try also...

Let  t  be the number of 6 month periods in the term.

7000( 1 + 4% * t )   =   1400 + 7000( 1 + 4% * t/2 )

Divide through by  7000.

1 + 4% * t   =   0.2 + 1 + 4% * t/2

Subtract  1  from both sides.

4% * t   =   0.2 + 4% * t/2

Subtract  4% * t/2  from both sides.

4% * t  -  4% * t/2   =   0.2

t(4%  -   4% / 2)   =   0.2

t(4% - 2%)   =   0.2

t( 2% )   =   0.2

t   =   0.2 / ( 2% )   =   10

There were  10  periods of 6 months in the term. That is  5  years.

Jan 14, 2018
edited by hectictar  Jan 14, 2018