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What is the difference between ordinary annuities, annuities due, perpetuities and uneven cash flows?

What is the difference between ordinary annuities, annuities due, perpetuities and uneven cash flows?

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Expert Solution

In general, annuities are regular &fixed /equal amounts of cash inflows or outflows ,over a period of time.
COMPARISON ISSUES Ordinary annuity Annuities due Perpetuity Uneven cash flows
Meaning Cash flows occur at the end of the period starting from the period t=1 Cash flows occur at the beginning of the period starting from t=0 An annuity that goes on forever Not equal in amounts of cash flows nor regular in periodicity of their occurence
Term Fixed & Specified Fixed & Specified Unending-perpetual or indefinite Fixed & Specified
Payment/receipt belongs to the period preceding the date of the cash in/out flow the period following the date of the cash in/out flow both are possibilities both are possibilities
Present value formula PV=X*(1-(1+r)^-n)/r PV=X*(1-(1+r)^-n)/r*(1+r) PV=X/r PV=x/(1+r)^1+y/(1+r)4+……z/(1+r)^n
Future Value formula FV=X*((1+r)^n-1)/r FV=X*((1+r)^n-1)/r*(1+r) Cannot be calculated as n is not known FV=X*(1+r)^(n-1)+y*(1+r)^(n-4)+…….z

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