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

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.

• 5% annually is a little high for something guaranteed, albeit given the 'perpetuity' aspect of forced contributions perhaps this isn't so unbelievable. How are you meant to retrieve the funds? Do you have the right to remove all your funds at any point? If you are, then I would be skeptical of whether this might be a scam, depending on if 5% is high in whatever your jurisdiction is. Mar 30 at 18:43

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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