<p>You are not considering compound interest. From <a href="https://en.wikipedia.org/wiki/Compound_interest" rel="nofollow noreferrer">Wikipedia</a>.:</p>
<blockquote>
<p>Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest.
<br>
[...] <br>
Compound interest is contrasted with simple interest, where previously accumulated interest is not added to the principal amount of the current period, so there is no compounding.</p>
</blockquote>
<p>In your case the daily interest would be
<span class="math-container">$$
\left( \sqrt[365]{1+\frac{7}{100}} - 1\right) \cdot \text{principal}.
$$</span>
This way the daily interest rate comes out to approximately <br>
0.00018538... <br>
Your method yielded <br>
0.00019178... <br>
so there is a small but significant difference.</p>

CC BY-SA 4.0
2021-06-12T17:50:27.633Z
nitpicking, but the daily _interest_  would be that formula, `- principal`
njzk2
CC BY-SA 4.0
2021-06-12T17:58:23.523Z
@njzk2 Well nitpicked!
Giskard
CC BY-SA 4.0
2021-06-09T07:21:44.777Z
2021-06-12T17:58:08.217Z
2021-06-12T17:58:08.217Z
Giskard
<p>If an institution is giving me an interest of 7% pa and the interest will be earned daily. How do I calculate how much do I earn per day?</p>
<p>I tried it calculate like this:</p>
<pre><code>(7/100)/365 * PRINCIPAL = my daily interest
</code></pre>
<p>That was my assumption - however, when I received the daily interest, the  amount was lower than I calculated with using the formula above.</p>
<p>What am I doing wrong?</p>

<interest-rate>
I am given an annual interest on my money. How do I calculate how much interest I earn daily?
user984621
# I am given an annual interest on my money. How do I calculate how much interest I earn daily?

(Asked by: username_0 on 2021-06-09)

If an institution is giving me an interest of 7% pa and the interest will be earned daily. How do I calculate how much do I earn per day?
I tried it calculate like this:
(7/100)/365 * PRINCIPAL = my daily interest

That was my assumption - however, when I received the daily interest, the  amount was lower than I calculated with using the formula above.
What am I doing wrong?

**Tags:** interest-rate


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## 1 answers

### Answer by username_1 on 2021-06-09. Score: 3

You are not considering compound interest. From [Wikipedia](https://en.wikipedia.org/wiki/Compound_interest).:

> Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest.
>   
> [...]   
> Compound interest is contrasted with simple interest, where previously accumulated interest is not added to the principal amount of the current period, so there is no compounding.

In your case the daily interest would be
$$
\left( \sqrt[365]{1+\frac{7}{100}} - 1\right) \cdot \text{principal}.
$$
This way the daily interest rate comes out to approximately   
0.00018538...   
Your method yielded   
0.00019178...   
so there is a small but significant difference.

> **Comments:**
> **username_2**: nitpicking, but the daily _interest_  would be that formula, `- principal`  
> **username_1**: @username_2 Well nitpicked!  

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