Question

A monthly perpetuity of $100 will start 6 months from today. If the discount rate is 6% APR compounded monthly, what is the value of the perpetuity today (at time t=0)?

Enter answer as a dollar, rounded to nearest dollar.

Answer 1

$ 19,410

Step-1:Value of perpetuity 6 months from today
Value of perpetuity 6 months from today	=	Monthly Cash flow	/	Monthly Discount rate
	=	$             100	/	0.005
	=	$       20,000
Working:
Monthly Discount rate	=	6%/12
	=	0.005
Step-2:Value of money today
Today's Value	=	Value of money 6 months from now	*	Discount factor
	=	$       20,000	*	0.970518
	=	$       19,410
Working:
Discount factor	=	(1+i)^-n		Where,
	=	(1+0.005)^-6	i	=	0.005
	=	0.97051808		n	=	6