# Thread: What have I done wrong in this rearrangment

1. ## What have I done wrong in this rearrangment

To make $\displaystyle i$ the subject of the following equation, these are my workings

$\displaystyle r=[1+i/12]^{12}-1$

1. Add 1 to both sides

$\displaystyle r+1=[1+i/12]^{12}$

2. Open the brackets so that

$\displaystyle r+1=1+i^{12}/12^{12}$

3. Then multiply both sides by $\displaystyle 12^{12}$ to give

$\displaystyle 12^{12}(r+1)=1+i^{12}$

4. And then finally

$\displaystyle 12^{1/12}(r+1)-1=i$

The answer in the book though is

$\displaystyle 12((r+1)^{1/12})-1=i$

But I don't understand why I was supposed raise$\displaystyle (r+1)$ to the power of 12 when I multiplied by $\displaystyle 12^{12}$ in step 3

2. Are you sure that you posted the correct statement.
For one: $\displaystyle \left( {1 + \frac{i}{{12}}} \right)^{12} \ne 1 + \frac{{i^{12} }}{{12^{12} }}$. It is much more complicated.
I don't think it is a pre-algebra/elementry algebra question.
What level question is this?

3. Is that my mistake then

why is

$\displaystyle \left( {1 + \frac{i}{{12}}} \right)^{12} \ne 1 + \frac{{i^{12} }}{{12^{12} }}$

4. Originally Posted by cistudent
why is
$\displaystyle \left( {1 + \frac{i}{{12}}} \right)^{12} \ne 1 + \frac{{i^{12} }}{{12^{12} }}$
I told that it is much more complicated.
Do you understand the binominal expansion theorem?
$\displaystyle \left( {1 + \frac{i}{{12}}} \right)^{12} = \sum\limits_{k = 0}^{12} {\binom{12}{k}\left( {\frac{i}{{12}}} \right)^k }$.

So either you have posted the wrong problem or you are not ready to work it.

5. OK this is the problem word for word and is included in a series of essential maths exercises all of which I got right except for this one. The binominal expansion theorem has not been mentioned thus far in the text book, so I'm guessing I wrote the problem wrong and am missing something obvious.

When interest is paid by monthly instalments, at a nominal rate of $\displaystyle i\%$ the actual rate of interest (the annual percentage rate) is

$\displaystyle r= \left( {1 + \frac{i}{{12}}} \right)^{12} - 1$

Express the nominal rate as a function of $\displaystyle r$.

My workings and the answer are as per the OP.

6. Sorry, but I thought you were working with mathematics.
That appears to have something to do with finance.
I cannot help with that. It is not mathematics.

7. Eh? Finance is Maths.

Is the problem not a practical application of mathematics? Perhaps I have put this in the wrong thread?