Question

Use the fact that the present value of a perpetuity paying $X per period starting in one year is

X/r, where r is the riskless rate of return, to determine the present value of annual payments of

$X accruing for 20 years, starting one year from now. Hint: Think of it as a perpetuity less the

appropriately discounted value of a perpetuity starting 20 years from now.

Answer 1

Annual payment=X

Risk less rate of return=r

We know that

Present value of perpetuity=X/r

Now we need to calculate the PV of annual payments of $X for 20 years. It is equal to PV of perpetuity less the PV of perpetuity of annual amount $X starting at the end of 21st year.

So,

PV of annual payments for 20 years=(X/r)-(X/r)*[1/(1+r)²⁰]=(X/r)[1-1/(1+r)²⁰]