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## #1 2014-01-23 23:20:31

Ian
Member
Registered: 2014-01-23
Posts: 5

### Compound Interest Derivatives

I have problem with two calculations of compound interest, as per my prescribed textbooks, which I find confusing:

1.
Q: Sam borrowed R10 000 at 7,5% per year compounded monthly. Determine the amount that Sam owes after 3 years.

A:  S = P(1+i)n
= 10000(1+7,5%)3
= 10000(1+0,075)3
= 12422,97

*Above, i and n have not been compounded monthly. My calculation is as follows:

S = P(1+i)n
= 10000(1+7,5%/12)3x12
= 10000(1+0,075/12)3x12
= 12514.46

2.
Q: Jill invested R10 000 into an account earning 9,2% interest, compounded quarterly. If she received R24 832,78 determine the periods under consideration.

A:               S = P(1+i)n
24832,78 = 10000(1+ 9,2%/4)n
n = 40/10
= 10 years

* This answer above is copied verbatim, no additional steps of calculation have been included in the prescribed textbook. My calculation, as per your formula provided on the website, is as follows:

n = In(24832.78/10000)/In(1+0.092)
= 10.33

When I do the calculations backwards by replacing n with 10 and 10.33 respectively my answers are also incongruent:

10: S=24832.78
10.33: S = 25589.46

Am I making basic errors or is the textbook wrong?

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## #2 2014-01-23 23:44:57

bob bundy
Registered: 2010-06-20
Posts: 8,337

### Re: Compound Interest Derivatives

hi Ian,

Welcome to the forum.

I'm from the UK and, as far as I'm aware, the periodic compound interest formula is not used.  Are you from the US ?

The topic is covered here:

http://www.mathsisfun.com/money/compoun … iodic.html

You would get slightly differing results using the 'correct' monthly rates of interest.

S = P(1+i)n
= 10000(1+7,5%)3
= 10000(1+0,075)3
= 12422,97

this is wrong for two reasons:

(i) the 1 + 7.5% is a multiplier so that should be 'raise to the power 3' not 'times by 3'

(ii) but the 7.5% is wrong too, as the compounding should be monthly.

I like your answer better but again the 3x12 is a power.

In number (2) that looks completely wrong.  For a start 40/10 is not 10.

LATER EDIT:

I've calculated the first question myself and get the same answer as you.  I guess you meant 'raise to the power' after all.

For the second one I assumed that 9.2% was per year and so divided by 4 to get the quarterly rate.

Hence n = 4.39 quarters.

I suggest you ignore the book and use the MIF page above to learn this.

Bob

Last edited by bob bundy (2014-01-24 00:03:47)

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #3 2014-01-24 00:17:44

Ian
Member
Registered: 2014-01-23
Posts: 5

### Re: Compound Interest Derivatives

Hi Bob,

Thanks for your polite correspondence and reassurance. I tend to second-guess myself when my calculations are (seemingly) off.

I'm South African. The link below says it all:

http://www.bdlive.co.za/national/education/2013/10/20/standard-of-maths-teaching-in-sa-at-rock-bottom-report-shows

Ian

Last edited by Ian (2014-01-24 00:20:09)

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## #4 2014-01-24 01:14:47

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Compound Interest Derivatives

Hi Bob;

Good Afternoon!

Hi Ian;

Welcome to the forum.

The 40/10 = 10 years is poor notation but I think they are not dividing. They are saying 40 quarters is 10 years. That is what the / probably means.

Ian wrote:

My calculation, as per your formula provided on the website, is as follows:

n = In(24832.78/10000)/In(1+0.092)
= 10.33

You have not used that formula correctly.This is how:

This is verified by direct calculation.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #5 2014-01-24 01:25:28

Ian
Member
Registered: 2014-01-23
Posts: 5

### Re: Compound Interest Derivatives

Hi Bobb;

Got it, thanks. I did not divide the given interest rate by the number of compounding periods per year. It seems I failed to apply the very thing lacking from the first question, to the second.

Last edited by Ian (2014-01-24 01:27:17)

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## #6 2014-01-24 01:37:45

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Compound Interest Derivatives

Okay, very good!

You will be interested to know that your educational system can not top the one they have in place over here. Whatever is bad in the world we have more of. Our educational system turns out people who can not even read or write beyond the ability of a 2 year old. This is not always bad, they all enter the legal profession and eventually end up in the US senate.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #7 2014-01-24 08:05:49

bob bundy
Registered: 2010-06-20
Posts: 8,337

### Re: Compound Interest Derivatives

hi Ian and bobbym

I wrote:

Hence n = 4.39 quarters.

Oh boy.  How did I get that?  It seemed unlikely at the time but I used a calculator so it must be right !

How many times have I told pupils not to rely on that excuse.

I've re-calculated it and get 39.9986.......

As you got that too bobbym, I think I'll stick with that answer.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #8 2014-01-24 13:53:43

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Compound Interest Derivatives

Hi Bob;

Happens to me all the time.

Where do these calculators come from and why are they here? In the night, in the dark, while we slumber, do they watch us? Where do they go when no one is watching them? Do not be fooled by their small size, their attractive cases, they are plotting. I think you see the problem now. Remain vigilant and we will triumph!

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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