# How to calculate price of a monthly perpetuity given the annual rate compounded monthly?

How would I go about calculating a perpetuity, lets say with monthly cash flows of $100 and a current interest rate of 7% per year compounded monthly if the first cash flow occurs at the end of month 4?

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- Anonymous8 months ago
You have a PATTERN of putting homework questions where they don't belong. STOP IT B I T C H.

- olliverLv 68 months ago
Present value of a perpetuity is PV = Pmt / i

This needs discounting back from period 4

PV = (Pmt / i) / (1+i)^4

PV = (100 / (7%/12)) / (1+7%/12)^4 = 16,748.62

- Don GLv 78 months ago
A monthly annuity of $100 forever, earning interest at .5833% per month, will require an investment of 17,143.84. If the investment is made 4 months before the first annuity payment, then with a FV of 17,143.84, N 4, R .5833%, its PV (the actual investment required) = 16,749.61.

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