How to calculate perpetuity when interest calculation interval is different from the cashflow interval

Question

I’m trying to calculate the present value of an investment scheme I was suggested with.
The scheme is, I have to invest say $100 in every quarter perpetually. Now I know how to calculate it (the present value of the investment) if the interest was also calculated quarterly.
But according to my adviser the interest is calculated monthly at a 5% p.a.
Tried to calculate but couldn’t. Any advise from the financial experts on calculating something like this? A formula would be very helpful.
Thanks in advance!

Chris Degnen · Answer

Your annual nominal rate compounded monthly is 5%, so
m = 0.05/12
a = (1 + m)^12 - 1     = 0.0511619
q = (1 + a)^(1/4) - 1  = 0.0125522

Where
m = monthly rate
a = annual effective rate
q = quarterly rate

So the annual nominal rate compounded quarterly is 4 q = 5.02086 %
Now you have an interest calculation interval that is the same as your cashflow interval.
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see also Effective Annual Rate Calculation

How to calculate perpetuity when interest calculation interval is different from the cashflow interval

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