This is the example that my teacher gave in my economic class. I will write the formula and equation with the given answer below. Actually my teacher already calculate the example table of (modified internal rate of return - mirr). The only thing that I don't know is how to use the formula or get the answer even though the answer is already given.
Example
Formula for Compound Amount
S = P (1+i)^n,
i = 12%
Answer
Product F
16,431.7 = 9000(1+i)^4 = 16.24%
MY PROBLEM
The problem is can you show me the exact longer way to get those '16.24%'? I know that I'm stupid but please help me. I'm really can't remember how to calculate it.
*what should I do with that '16431.7'? *how to get that '16.24%'?
Given $P=9000$, $i=12\,\%$, $n=4$, we first write $12\,\%$ as $\frac {12}{100}$ and then compute $$ \begin{align}S&=P\cdot (1+i)^n\\&=9000\cdot\left(1+\frac{12}{100}\right)^4\\&=9000\cdot 1.12^4 \\&= 9000\cdot 1.57351936 \\&= 14161.67424\end{align}$$ which I do not see in your post.
Perhaps, your actual task rather was: Given $S=16431.7$, $P=9000$, $n=4$, find $i$? For this, transform the orignal equation: $$P\cdot (1+i)^n=S$$ $$ (1+i)^n= \frac SP$$ $$ 1+i = \sqrt[n]{\frac SP}$$ $$ i = \sqrt[n]{\frac SP}-1$$ so $$ \begin{align}i&=\sqrt[4]\frac{16431.7}{9000}-1 \\&\approx\sqrt[4]{\strut1.82574}-1\\&\approx 1.1624-1\\&=0.1624\\&=16.24\,\% \end{align}$$