# What have I done wrong in this rearrangment

#### cistudent

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

#### Plato

MHF Helper
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?

#### cistudent

Is that my mistake then

why is

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

#### Plato

MHF Helper
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.

#### cistudent

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.

#### Plato

MHF Helper
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.

#### cistudent

Eh? Finance is Maths.

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