# Calculating long intervals of Interest with Simple Interest Formula

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

## 1 Answer

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.