What have I done wrong in this rearrangment

May 2010
11
0
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
Aug 2006
22,508
8,664
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?
 
May 2010
11
0
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
Aug 2006
22,508
8,664
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.
 
May 2010
11
0
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
Aug 2006
22,508
8,664
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.
 
May 2010
11
0
Eh? Finance is Maths.

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