Initial capital

layla_nt30

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Joined
Mar 18, 2023
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3
Hello,
I am quite confused about this question:
"A capital raised €53444,75 at an annual compound interest rate of 13% for 50 years. What was the initial capital (accurate to 2 decimal places)? (Notice the answer is not 118,57)"
I've thought about this carefully, but I really can't get beyond 118,57
I used this formula: k = K / (1 + i)^n = 53444,75 / (1 + 13%)^50 = 118,57

Many thanks in advance if anyone can answer this
 
Hello,
I am quite confused about this question:
"A capital raised €53444,75 at an annual compound interest rate of 13% for 50 years. What was the initial capital (accurate to 2 decimal places)? (Notice the answer is not 118,57)"
I've thought about this carefully, but I really can't get beyond 118,57
I used this formula: k = K / (1 + i)^n = 53444,75 / (1 + 13%)^50 = 118,57

Many thanks in advance if anyone can answer this
Hi @layla_nt30,

Just as you say,
\(\displaystyle 53,444.75 ÷ 1.13^{50}\) does, indeed, equal \(\displaystyle 118.57\).

Please post the problem as it was presented in its entirety* and also the answer (that is not 118.57) that was provided with it; someone may then be able to offer further advice.

*A picture should suffice if you cannot copy out all the text/diagrams (if included).

Regards.
 
Hello,
I am quite confused about this question:
"A capital raised €53444,75 at an annual compound interest rate of 13% for 50 years. What was the initial capital (accurate to 2 decimal places)? (Notice the answer is not 118,57)"
I've thought about this carefully, but I really can't get beyond 118,57
I used this formula: k = K / (1 + i)^n = 53444,75 / (1 + 13%)^50 = 118,57

Many thanks in advance if anyone can answer this
The wording seems a little odd. Can you show us how the phrase "a capital raised ..." is defined in your class? (Or [perhaps a worked example with similar wording.)

I would take it to mean that the initial amount of capital (which you are to find) resulted in either a final amount of €53444,75, or perhaps interest of €53444,75. You have assumed the former, so the only idea I have is to try the latter.
 
The wording seems a little odd. Can you show us how the phrase "a capital raised ..." is defined in your class? (Or [perhaps a worked example with similar wording.)

I would take it to mean that the initial amount of capital (which you are to find) resulted in either a final amount of €53444,75, or perhaps interest of €53444,75. You have assumed the former, so the only idea I have is to try the latter.
@layla_nt30,

@Dr.Peterson raises a very good possible alternative interpretation.

So is the answer (you've been given) €118.84?

If so, can you work out how you would arrive at that answer?
 
Hi @layla_nt30,

Just as you say,
\(\displaystyle 53,444.75 ÷ 1.13^{50}\) does, indeed, equal \(\displaystyle 118.57\).

Please post the problem as it was presented in its entirety* and also the answer (that is not 118.57) that was provided with it; someone may then be able to offer further advice.

*A picture should suffice if you cannot copy out all the text/diagrams (if included).

Regards.
This is all I could find, our teacher only makes one exercise and we don't really see much theory. And I am aware that some of the wording can be strange because our teacher is somewhat unique
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@layla_nt30,

@Dr.Peterson raises a very good possible alternative interpretation.

So is the answer (you've been given) €118.84?

If so, can you work out how you would arrive at that answer?
I thought just using the classic formula.
I have used this formula in Excel, as I was taught: k = K / (1 + i)^n = 53444,75 / (1 + 13%)^50 = 118,57
But I still got this answer, and from there on I've been stuck.
 
This is all I could find, our teacher only makes one exercise and we don't really see much theory. And I am aware that some of the wording can be strange because our teacher is somewhat unique
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I think you need to ask your teacher what the problem means. Since the wording is not explained, such a request is reasonable. And since the question explicitly tells you that the result you get from the formula is wrong, some subtlety in the wording is the whole point.

The rest of the wording here is standard (to the extent I know financial terminology, which I don't), except that "over 12 years" would suggest to me an annuity rather than an amount payable after 12 years.
 
I thought just using the classic formula.
I have used this formula in Excel, as I was taught: k = K / (1 + i)^n = 53444,75 / (1 + 13%)^50 = 118,57
But I still got this answer, and from there on I've been stuck.
Hi @layla_nt30.

These exercises are (usually) designed to encourage students to acquire an understanding of the relationships between capital, investments, returns, interest accrued, capital gains and interest rates. The idea is to steer you away from the use of a "formula" and to use your understanding of the relationships between these things to solve problems where things get presented differently.

As you can see, the use of your "formula" does not get the desired answer in this case (a fact that the question warns you about in advance!).

The question specifically states that €118.57 is not the answer but is the required answer provided anywhere?

If we can see what answer they are actually looking for we can probably work 'backwards' from that to explain what the question really means; at present, that is evidently quite obscure as neither of the interpretations so far considered appears to be correct.

Is the answer wanted given anywhere?
 
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If no answer is provided, can you see how the answer I suggested above (€118.84) is arrived at? ?

That would provide you with a useful little exercise in handling these kind of problems even if it's not what this question actually means. ?
 
The wording is not standard in U.S. finance.

”A capital raised x” makes absolutely no sense. Capitals do not raise money.

Moreover, if what is being talked about is a DEBT, it would be very unlikely as well as imprudent to contract for no payments to be made for 50 years. The closest such debt instruments are UK “consols,” which pay periodic fixed interest but are never required to pay principal.
 
The wording is not standard in U.S. finance.
The OP clearly isn't operating in the 'world' of "U.S. finance"; the question deals with Euros!
”A capital raised x” makes absolutely no sense. Capitals do not raise money.
I have little familiarity with "U.S. finance" but this makes perfect sense to me and, no doubt, to anyone else in Europe! "Capital" is widely referred to (here, anyway) as an (initial) sum invested as a means of earning a return (interest) on it hence the term "Capital Gain" as earnings that are widely taxed by governments. Capital is also widely referred to here as money raised to fund a particular project.
Moreover, if what is being talked about is a DEBT, it would be very unlikely as well as imprudent to contract for no payments to be made for 50 years. The closest such debt instruments are UK “consols,” which pay periodic fixed interest but are never required to pay principal.
There was no mention of "DEBT" anywhere in the OP and the extended period involved here is, clearly, one that has been chosen by the author(s) simply to provide an exercise in dealing with this kind of problem. However, it might well be quite applicable in real life were one to wish to calculate what sum had initially been deposited in a bank account (involved in probate for example) when it had earned a substantial level of interest over such a period.

I am unsure what you hope to contribute to this thread by your comments, @NotJeffM. ?
 
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The OP clearly isn't operating in the 'world' of "U.S. finance"; the question deals with Euros!

I have little familiarity with "
U.S. finance" but this makes perfect sense to me and, no doubt, to anyone else in Europe! "Capital" is widely referred to (here, anyway) as an (initial) sum invested as a means of earning a return (interest) on it hence the term "Capital Gain" as earnings that are widely taxed by governments. Capital is also widely referred to here as money raised to fund a particular project.

There was no mention of "
DEBT" anywhere in the OP and the extended period involved here is, clearly, one that has been chosen by the author(s) simply to provide an exercise in dealing with this kind of problem. However, it might well be quite applicable in real life were one to wish to calculate what sum had initially been deposited in a bank account (involved in probate for example) when it had earned a substantial level of interest over such a period.

I am unsure what you hope to contribute to this thread by your comments, @NotJeffM. ?
What I am contributing is helping the student understand that their confusion is perfectly understandable. The student’s teacher eeither knows nothing about finance or knows nothing about the English language (or probably knows nothing about both). However you define capital, it does not have agency; it does not raise money by going to the bank or floating stock on a bourse. Nor does it open a savings account at a building society. Those are activities that human actors engage in. So the sentence is practical nonsense from its subject to its final period.

Although there are many forms in which capital is treated legally, the ones most common in Europe and North America are debt and equity. And most forms of equity do not have a constant return to which the mathematics of annuities, etc. apply. Thus, for anyone who actually knows something about how finance is conducted in most of the commercial world, defined rates of return are associated with debt. And debt has periodic payments if it involves maturities measured in decades. (You might try getting your bank to lend you money without a single payment of interest or principal for just a single decade.)

Students who study the mathematics of finance do so with some limited understanding of the mechanics and vocabulary of lending in the real commercial world. Problems that violate that understanding do not help students. I had a career in finance for 43 years, and I have no idea what actual situation that problem contemplates. That makes it extremely difficult to construct a reasonable mathematical model to use.

You have suggested reverse engineering from the given answer to determine what the teacher intended to ask. This hardly teaches how to use mathematics to find answers. Moreover, it is not clear that any answer was provided on which to do reverse engineering. Maybe the teacher should have made the effort and taken the time to pose a question from which an answer can be derived rather than vice versa.
 
What I am contributing is helping the student understand that their confusion is perfectly understandable. The student’s teacher eeither knows nothing about finance or knows nothing about the English language (or probably knows nothing about both). However you define capital, it does not have agency; it does not raise money by going to the bank or floating stock on a bourse. Nor does it open a savings account at a building society. Those are activities that human actors engage in. So the sentence is practical nonsense from its subject to its final period.

Although there are many forms in which capital is treated legally, the ones most common in Europe and North America are debt and equity. And most forms of equity do not have a constant return to which the mathematics of annuities, etc. apply. Thus, for anyone who actually knows something about how finance is conducted in most of the commercial world, defined rates of return are associated with debt. And debt has periodic payments if it involves maturities measured in decades. (You might try getting your bank to lend you money without a single payment of interest or principal for just a single decade.)

Students who study the mathematics of finance do so with some limited understanding of the mechanics and vocabulary of lending in the real commercial world. Problems that violate that understanding do not help students. I had a career in finance for 43 years, and I have no idea what actual situation that problem contemplates. That makes it extremely difficult to construct a reasonable mathematical model to use.

You have suggested reverse engineering from the given answer to determine what the teacher intended to ask. This hardly teaches how to use mathematics to find answers. Moreover, it is not clear that any answer was provided on which to do reverse engineering. Maybe the teacher should have made the effort and taken the time to pose a question from which an answer can be derived rather than vice versa.
All very true and an insightful exposition on financial matters. (Are you sure you are not JeffM???)

But does introducing all this really "help" the OP? It looks to me like s/he is just working on exercises in the calculation of future/past sums that are subject to compound interest over given time periods (or where those time periods themselves are to be determined).

It also looks like @layla_nt30 may have given up/lost interest/set it aside for another day or gone away (on holiday rather than died or otherwise similarly indisposed) so I doubt if there's much point in either of us adding anything further to this thread but thank you for taking the time to expand on your reasoning. ?
 
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