<p>The official answer explains it correctly. A nominal interest rate is calculated independent of inflation. \$25 = \$20 (1 + 0.25).</p>

<p>I cannot follow the logic of your calculations, as they do not correspond to how a real rate of interest is calculated. The real rate of interest is the nominal interest rate less inflation, or 15%.</p>

CC BY-SA 4.0
2020-04-07T17:53:09.440Z
"The real rate of interest is the nominal interest rate less inflation". Not applicable if we don't know the nominal interest rate in the first place. Do you have formulas/ideas for cases when we don't know the nominal rate?
KarmaPeasant
CC BY-SA 4.0
2020-04-07T18:34:01.050Z
The nominal rate was calculated in the official answer, and my answer - 25%. Lent \$20, got back \$25.
Brian Romanchuk
CC BY-SA 4.0
2020-04-07T17:31:05.350Z
2020-04-07T17:31:05.350Z
Brian Romanchuk
<p>Have you considered that the nominal interest rate is the rate of interest without adjusting for inflation? So repaying \$25 on \$20 comes to an interest of 25%, no inflation adjustment is needed.</p>

CC BY-SA 4.0
2020-04-07T17:54:23.427Z
"Have you considered that the nominal interest rate is the rate of interest without adjusting for inflation?" But I didn't adjust it! I adjusted the initial sum of money.
KarmaPeasant
CC BY-SA 4.0
2020-04-07T18:05:54.403Z
By the way, I used the same logic to solve similiar problem and it seems like I was able to solve it correctly: "Ygritte loaned Mans \$100. Mans paid her back \$110 one year later. The annual rate of inflation was 3%, percent.
What was the nominal interest rate that Ygritte earned on this loan?" My answer: At first we find the real interest rate, it's 7/110. Then we round it and get 7% of real interest rate. Then we add 3% of inflation. Thus we get 10% of the nominal interest rate. I used method from here: https://youtu.be/cNm196bVE5A
KarmaPeasant
CC BY-SA 4.0
2020-04-07T18:09:28.960Z
I just don't understand why this method gives correct answer for problem with Ygritte, but wrong with Daenerys. Problems seem identical
KarmaPeasant
CC BY-SA 4.0
2020-04-07T17:26:52.957Z
2020-04-07T17:26:52.957Z
Giskard
<p>Keep in mind that nominal interest rate=Profit/Initial Amount.</p>

<p>The exact relationship that links real interest rate, nominal interest rate and inflation is <span class="math-container">$(1+R_{nominal})=(1+R_{real})(1+\pi)$</span> where <span class="math-container">$\pi$</span> is the inflation rate (Known as Fisher's identity)</p>

<p><span class="math-container">$R_{nominal}=R_{real}+\pi$</span> is an approximation that works best when those variables are relatively small.</p>

CC BY-SA 4.0
2020-04-08T16:30:59.127Z
"Keep in mind that nominal interest rate=Profit/Initial Amount". Thanks! Not only it works with the example in the OP, but it also works this problem that I posted in comments where the lender was Ygritte.
KarmaPeasant
CC BY-SA 4.0
2020-04-08T19:29:16.117Z
A more general way of finding $i$ is by setting the present values equal, here that would mean 20=25/(1+i). But if they devised a different scheme, say Grey Worm has to pay 15 in one and two years, then the interest rate would be calculated by solving the equation $$20=\frac{15}{1+i}+\frac{15}{(1+i)^2}$$
actuarialboi9
CC BY-SA 4.0
2020-04-07T18:26:42.553Z
2020-04-07T18:26:42.553Z
actuarialboi9
<blockquote>
  <p><a href="https://i.sstatic.net/CIajF.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/CIajF.png" alt="enter image description here"></a></p>
</blockquote>

<p>My reasoning: The nominal interest rate = the real interest rate + the expected inflation rate. We need to calculate the nominal interest rate. We know the expected inflation rate, so the only problem is to calculate the real interest rate. In order to calculate the real interest rate we need to see how much money received is more than money given. And due to inflation we need to adjust the initial sum to inflation. 110 - 100*1.03=7, this is inflation-adjusted amount of money by which Daenerys will become richer. In order to calculate the real value we need do following: 7/110=0.0(63), which is about 6.4%. Thus the nominal rate equals 6.4+10=16.4</p>

<p>Here is the offical answer, but I'm afraid it doesn't make sense:</p>

<blockquote>
  <p><a href="https://i.sstatic.net/vsENq.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/vsENq.png" alt="Blockquote"></a></p>
</blockquote>

<interest-rate><credit>
Why does the nominal interest rate equal 25% in this problem, instead of 16.4%?
KarmaPeasant
# Why does the nominal interest rate equal 25% in this problem, instead of 16.4%?

(Asked by: username_0 on 2020-04-07)

> [![enter image description here](https://i.sstatic.net/CIajF.png)](https://i.sstatic.net/CIajF.png)

My reasoning: The nominal interest rate = the real interest rate + the expected inflation rate. We need to calculate the nominal interest rate. We know the expected inflation rate, so the only problem is to calculate the real interest rate. In order to calculate the real interest rate we need to see how much money received is more than money given. And due to inflation we need to adjust the initial sum to inflation. 110 - 100\*1.03=7, this is inflation-adjusted amount of money by which Daenerys will become richer. In order to calculate the real value we need do following: 7/110=0.0(63), which is about 6.4%. Thus the nominal rate equals 6.4+10=16.4

Here is the offical answer, but I'm afraid it doesn't make sense:

> [![Blockquote](https://i.sstatic.net/vsENq.png)](https://i.sstatic.net/vsENq.png)

**Tags:** interest-rate, credit


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## 3 answers

### Answer by username_3 on 2020-04-07. Score: 2 | Accepted answer

Keep in mind that nominal interest rate=Profit/Initial Amount.

The exact relationship that links real interest rate, nominal interest rate and inflation is $(1+R\_{nominal})=(1+R\_{real})(1+\pi)$ where $\pi$ is the inflation rate (Known as Fisher's identity)

$R\_{nominal}=R\_{real}+\pi$ is an approximation that works best when those variables are relatively small.

> **Comments:**
> **username_0**: "Keep in mind that nominal interest rate=Profit/Initial Amount". Thanks! Not only it works with the example in the OP, but it also works this problem that I posted in comments where the lender was Ygritte.  
> **username_3**: A more general way of finding $i$ is by setting the present values equal, here that would mean 20=25/(1+i). But if they devised a different scheme, say Grey Worm has to pay 15 in one and two years, then the interest rate would be calculated by solving the equation $$20=\frac{15}{1+i}+\frac{15}{(1+i)^2}$$  

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### Answer by username_1 on 2020-04-07. Score: 0

The official answer explains it correctly. A nominal interest rate is calculated independent of inflation. \$25 = \$20 (1 + 0.25).

I cannot follow the logic of your calculations, as they do not correspond to how a real rate of interest is calculated. The real rate of interest is the nominal interest rate less inflation, or 15%.

> **Comments:**
> **username_0**: "The real rate of interest is the nominal interest rate less inflation". Not applicable if we don't know the nominal interest rate in the first place. Do you have formulas/ideas for cases when we don't know the nominal rate?  
> **username_1**: The nominal rate was calculated in the official answer, and my answer - 25%. Lent \$20, got back \$25.  

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### Answer by username_2 on 2020-04-07. Score: 0

Have you considered that the nominal interest rate is the rate of interest without adjusting for inflation? So repaying \$25 on \$20 comes to an interest of 25%, no inflation adjustment is needed.

> **Comments:**
> **username_0**: "Have you considered that the nominal interest rate is the rate of interest without adjusting for inflation?" But I didn't adjust it! I adjusted the initial sum of money.  
> **username_0**: By the way, I used the same logic to solve similiar problem and it seems like I was able to solve it correctly: "Ygritte loaned Mans \$100. Mans paid her back \$110 one year later. The annual rate of inflation was 3%, percent. What was the nominal interest rate that Ygritte earned on this loan?" My answer: At first we find the real interest rate, it's 7/110. Then we round it and get 7% of real interest rate. Then we add 3% of inflation. Thus we get 10% of the nominal interest rate. I used method from here: https://youtu.be/cNm196bVE5A  
> **username_0**: I just don't understand why this method gives correct answer for problem with Ygritte, but wrong with Daenerys. Problems seem identical  

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