Question

If your required rate is 5%, how much is worth 10€ every year for 50 years? For ever?

Answer 1

A.

Let’s assume the cash flow will occur at the end of each year.

Present value of annuity is the present worth of cash flows that is to be received in the future, if future value is known, rate of interest in r and time is n then PV of annuity is

PV of annuity = P* [1- (1+ r) ^-n]/ r

Where,

              Periodic deposit (P) = $10

              Interest rate = 5%

              Time (n) = 50

Let's put all the values in the formula to find PV o annuity

= 10* [1- (1+ 0.05)^-50]/ 0.05

= 10* [1- (1.05)^-50]/ 0.05

= 10* [1- 0.087203727]/ 0.05

= 10* [0.912796273/ 0.05]

= 10* [18.25592546]

= 182.56

B.

If the cash flow will occur forever the PV will be

PV of perpetuity = annual cash flow/ required rate

                           = 10/ 0.05

                            = 200                                                                                  

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