# I am given an annual interest on my money. How do I calculate how much interest I earn daily?

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?

You are not considering compound interest. From Wikipedia.:

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...
• nitpicking, but the daily interest would be that formula, - principal Jun 12, 2021 at 17:50