How to calculate interest on Monthly Effective loans where duration greater than compounding

Question

I have an amortization software and trying to manually calculate the interest accrued it calculated.

The Key values are:

Compounding: Monthly
Nominal Annual Rate: 10%
Day Count: 365
Principal: 500,000
Disbursal: 01/01/2017 
Payment: 15/02/2017

Using the software, the interest accrued on 15/02/2017 is 6,100.46. I'm wondering how do i calculate that.

I tried two methods, both didn't quite work.

Method 1. Using daily effect rate

Interest accrued = 500,000 * .1 * 45 days / 365 days
                 = 6164.38

Method 2. Using a mixture. There's 1 full month payment + 14 extra days.

Interest Accrued for 1 month = 500,000 *.1 / 12
                             = 4166.67

Interest Accrued for 14 days = 500,00 *.1 * 14 / 365
                             = 1917.81

Total interest accrued = 4166.67 + 1917.81
                       = 6084.48

I was able to successfully match for situations where payments are made in exact compounding intervals or less, but not when it's more than compounding interval. Any help would be greatly appreciated.

Answer 1

Your second method is correct, you're just missing the compounding of the first month's interest when calculating the second month's interest:

Interest Accrued for 1 month = 500,000 *.1 / 12
                             = 4166.67

                                 V--- includes interest from first month
Interest Accrued for 14 days = 504,166 *.1 * 14 / 365
                             = 1933.79

Total interest accrued = 4166.67 + 1933.79
                       = 6100.46