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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%'?

Mathstupid
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1 Answers1

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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 $$ \begin{align}i&=\sqrt[4]\frac{16431.7}{9000}-1 \\&\approx\sqrt[4]{\strut1.82574}-1\\&\approx 1.1624-1\\&=0.1624\\&=16.24\,\% \end{align}$$

Hagen von Eitzen
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  • I'm still don't really know how this platform work but thank you for the one that answering my question. Yes, I need to find the (i) but I forgot and I don't really understand when my teacher give me a short form of calculation work to get the answer. Thank You so much to you. You had helped me a lot. Please bear with me because I had a feeling that I will ask a lot of stupid question in the future. – Mathstupid Dec 30 '20 at 05:45