I'm wondering how do I calculate the interest accrued if the intervals aren't perfect. For example

```
Principal - $100,000
Interest - 8%
Compounding monthly
Disbursal Date - January 1st, 2016
Initial Payment Date - February 11, 2016

```

I can calculate it if it's exactly 1 month then the time passed would be 1/12. 

Interest accrued = ((1 + i / cf)^(cf)\*T - 1) \* principal balance

Where cf is compound frequency, T is time. 

If duration that has passed is exactly 1 month, the interest accrued is 666.67. The interest accrued to the original question is $887.31, but I'm unsure how to get that value.

Answer's here <https://i.snag.gy/lMYorT.jpg>