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on a compound interest problem

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  on a compound interest problem Daniel Bastos <dbastos@toledo.com> - 2017-03-19 10:30 -0300
    Re: on a compound interest problem Barry Schwarz <schwarzb@dqel.com> - 2017-03-19 13:11 -0700
      Re: on a compound interest problem Daniel Bastos <dbastos@toledo.com> - 2017-03-19 20:15 -0300
        Re: on a compound interest problem Alla <vitale.alla@gmail.com> - 2017-06-06 10:30 +0300
          Re: on a compound interest problem Alla <vitale.alla@gmail.com> - 2017-06-06 10:34 +0300
            Re: on a compound interest problem Daniel Bastos <dbastos@toledo.com> - 2017-08-10 13:03 -0300

#4867 — on a compound interest problem

I say this problem's formula is incorrect, but I'd appreciate an expert
confirmation.

Problem.  Consider an amount q invested for n years at an interest rate j.  
The total amount after n years is given by the formula

  gf = q * ((1 + j/100) + (1 + j/100)^2 + ... + (1 + j/100)^n).

[...]

I think that's not correct.  The initial amount is q.  After 1 year, the
amount is

  q (1 + 1/100).  

After 2 years, the amount is

  q (1 + 1/100)^2

Why are they adding in their formula?  That formula seems like a very
good investment.  In fact, too good to be true.

Thank you!

(*) Note to self

After 2 years at 10% with q = 100. (* 100 (+ 1.10 (expt 1.10 2))) = 231.
(It should be 121.)

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#4868

On Sun, 19 Mar 2017 10:30:12 -0300, Daniel Bastos <dbastos@toledo.com>
wrote:

>I say this problem's formula is incorrect, but I'd appreciate an expert
>confirmation.
>
>Problem.  Consider an amount q invested for n years at an interest rate j.  
>The total amount after n years is given by the formula
>
>  gf = q * ((1 + j/100) + (1 + j/100)^2 + ... + (1 + j/100)^n).

This is the formula for q invested **each year** over a length of n
years.

>I think that's not correct.  The initial amount is q.  After 1 year, the
>amount is
>
>  q (1 + 1/100).  

This formula is for q invested **once** for n years.

>After 2 years, the amount is
>
>  q (1 + 1/100)^2
>
>Why are they adding in their formula?  That formula seems like a very
>good investment.  In fact, too good to be true.
>
>Thank you!
>
>(*) Note to self
>
>After 2 years at 10% with q = 100. (* 100 (+ 1.10 (expt 1.10 2))) = 231.
>(It should be 121.)

-- 
Remove del for email

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#4870

Barry Schwarz <schwarzb@dqel.com> writes:

> On Sun, 19 Mar 2017 10:30:12 -0300, Daniel Bastos <dbastos@toledo.com>
> wrote:
>
>>I say this problem's formula is incorrect, but I'd appreciate an expert
>>confirmation.
>>
>>Problem.  Consider an amount q invested for n years at an interest rate j.  
>>The total amount after n years is given by the formula
>>
>>  gf = q * ((1 + j/100) + (1 + j/100)^2 + ... + (1 + j/100)^n).
>
> This is the formula for q invested **each year** over a length of n
> years.

That's probably what the problem meant.  Thank you.

[...]

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#4976

On 3/20/17 02:15, Daniel Bastos wrote:
> Barry Schwarz <schwarzb@dqel.com> writes:
> 
>> On Sun, 19 Mar 2017 10:30:12 -0300, Daniel Bastos <dbastos@toledo.com>
>> wrote:
>>
>>> I say this problem's formula is incorrect, but I'd appreciate an expert
>>> confirmation.
>>>
>>> Problem.  Consider an amount q invested for n years at an interest rate j.
>>> The total amount after n years is given by the formula
>>>
>>>   gf = q * ((1 + j/100) + (1 + j/100)^2 + ... + (1 + j/100)^n).
>>
>> This is the formula for q invested **each year** over a length of n
>> years.
> 
> That's probably what the problem meant.  

You can see that by opening the brackets.
Using a simple example, where q = 100, n = 3, and rate 0.05

# invest 100 in the first year, and get the first year's future value of
   FV = 100 * 1.05 = 105

# at the end of the first year you add again 100 to those 105, and get 
at the end of the second year:
   (100 + 105) * 1.05 = 215.25

# at the end of the second year you add again 100 to 215.25, and get at 
the end of the third year:
   (100 + 215.25) * 1.05 = 331.01



-- 
Respectfully,
Alla

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#4977

On 6/6/17 10:30, Alla wrote:
> On 3/20/17 02:15, Daniel Bastos wrote:
>> Barry Schwarz <schwarzb@dqel.com> writes:
>>
>>> On Sun, 19 Mar 2017 10:30:12 -0300, Daniel Bastos <dbastos@toledo.com>
>>> wrote:
>>>
>>>> I say this problem's formula is incorrect, but I'd appreciate an expert
>>>> confirmation.
>>>>
>>>> Problem.  Consider an amount q invested for n years at an interest 
>>>> rate j.
>>>> The total amount after n years is given by the formula
>>>>
>>>>   gf = q * ((1 + j/100) + (1 + j/100)^2 + ... + (1 + j/100)^n).
>>>
>>> This is the formula for q invested **each year** over a length of n
>>> years.
>>
>> That's probably what the problem meant. 
> 
> You can see that by opening the brackets.
> Using a simple example, where q = 100, n = 3, and rate 0.05
> 
> # invest 100 in the first year, and get the first year's future value of
>    FV = 100 * 1.05 = 105
> 
> # at the end of the first year you add again 100 to those 105, and get 
> at the end of the second year:
>    (100 + 105) * 1.05 = 215.25
> 
> # at the end of the second year you add again 100 to 215.25, and get at 
> the end of the third year:
>    (100 + 215.25) * 1.05 = 331.01
> 

Sorry! I have only now noticed that it was posted in March, so I guess 
the issue is solved long time ago.


-- 
Respectfully,
Alla

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#4988

Alla <vitale.alla@gmail.com> writes:

> On 6/6/17 10:30, Alla wrote:
>> On 3/20/17 02:15, Daniel Bastos wrote:
>>> Barry Schwarz <schwarzb@dqel.com> writes:
>>>
>>>> On Sun, 19 Mar 2017 10:30:12 -0300, Daniel Bastos <dbastos@toledo.com>
>>>> wrote:
>>>>
>>>>> I say this problem's formula is incorrect, but I'd appreciate an expert
>>>>> confirmation.
>>>>>
>>>>> Problem.  Consider an amount q invested for n years at an
>>>>> interest rate j.
>>>>> The total amount after n years is given by the formula
>>>>>
>>>>>   gf = q * ((1 + j/100) + (1 + j/100)^2 + ... + (1 + j/100)^n).
>>>>
>>>> This is the formula for q invested **each year** over a length of n
>>>> years.
>>>
>>> That's probably what the problem meant. 
>>
>> You can see that by opening the brackets.
>> Using a simple example, where q = 100, n = 3, and rate 0.05
>>
>> # invest 100 in the first year, and get the first year's future value of
>>    FV = 100 * 1.05 = 105
>>
>> # at the end of the first year you add again 100 to those 105, and
>> get at the end of the second year:
>>    (100 + 105) * 1.05 = 215.25
>>
>> # at the end of the second year you add again 100 to 215.25, and get
>> at the end of the third year:
>>    (100 + 215.25) * 1.05 = 331.01
>
> Sorry! I have only now noticed that it was posted in March, so I guess
> the issue is solved long time ago.

The OP is still here and appreciates your posting.  Thank you!

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