Future value Given an interest rate r the future value one period from now of $1 is FV=1+r Given an interest rate r the future value one period from now of sm is FV=m(1+r)
Future Value Given an interest rate r the future value one period from now of $1 is Given an interest rate r the future value one period from now of $m is FV = 1+ r. FV = m(1+ r)
Present value(现值) Suppose you can pay now to obtain $1 at the start of next period What is the most you should pay? $1? No. If you kept your $1 now and saved it then at the start of next period you would have $(1+r)>$1,so paying $1 now for $1 next period is a bad deal
Present Value （现值） Suppose you can pay now to obtain $1 at the start of next period. What is the most you should pay? $1? No. If you kept your $1 now and saved it then at the start of next period you would have $(1+r) > $1, so paying $1 now for $1 next period is a bad deal
Present value Q: How much money would have to be saved now, in the present, to obtain $1 at the start of the next period? A: Sm saved now becomes $m(1+r)at the start of next period, so we want the value of m for which m(1+r)=1 That is, m=1/(1+r), the present-value of $1 obtained at the start of next period
Present Value Q: How much money would have to be saved now, in the present, to obtain $1 at the start of the next period? A: $m saved now becomes $m(1+r) at the start of next period, so we want the value of m for which m(1+r) = 1 That is, m = 1/(1+r), the present-value of $1 obtained at the start of next period
Present value The present value of $1 available at the start of the next period is PV 1+r And the present value of $m available at the start of the next period is PV= 1+r
Present Value The present value of $1 available at the start of the next period is And the present value of $m available at the start of the next period is PV r = + 1 1 . PV m r = 1+
Present value E.g., if r= 0.1 then the most you should pay now for $1 available next period is PV =S0.91 1+0·1 And if r=0.2 then the most you should pay now for $1 available next period is PV =S0.83 1+0·2
Present Value E.g., if r = 0.1 then the most you should pay now for $1 available next period is And if r = 0.2 then the most you should pay now for $1 available next period is PV = + = 1 1 0 1 $0 91. PV = + = 1 1 0 2 $0 83