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My last post Calculating long intervals of Interest calculates interest using compounding formula. But what about calculating simple interest accrued where the day count is actual/actual and it goes through two different year lengths (365 to 366 or vice versa)

For example

What is the interest accrued between December and January

Loan has principal of $100,000
Interest rate of 8% compounding annually
Disbursal Date is December 15 2015
Initial Payment Date is January 15 2016

What I would normally do

Interest Accrued = Principal * Interest * Time
                 = 40000 * 0.085 * 31/366

What I think it should be but I'm not entire sure

2015 has 16 days
2016 has 15 days

Time = 16/365 + 15/366

Interest Accrued = Principal * Interest * Time
                 = 40000 * 0.085 * (16/365 + 15/366)

Is this the correct way of calculating interest with two different year intervals when it has actual/actual

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It depends of what day count convention you are using, it seems that the formula your are is the Actual/Actual ISDA formula. But since there is more than one form of doing this, I don't think there is a truly correct way.

IMO, if you don't have any particular reason to not do so, I'd rather stick with the conventional 365 days a year.

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