YES, its true.. its actually a part of the fine prints in your mortgage..
When you take a variable rate mortgage, some lenders have an option (or allow you to choose from)...
1. Increase/Decreasing the monthly payment with every increase/decrease in interest rates. or
2. Keep the same monthly payment & change the principal amount paid every month with every increase or decrease in interest rates.. with this though there is a threshold, that once the interest portion of the monthly payment reaches a certain level (& principal portion becomes negligible), they increase the monthly payment..
Yours is the first option, where its increasing $40 with an increase in interest rate; whereas the previous post has the other option in her/his mortgage..