Economics-
202- UKZN
Investments
People value their present consumption more than their future consumption hence people
need incentives to delay their consumption.
People would prefer to have their money today grown by X amount to incentivize the
delay in consumption. This is because of positive time preferences.
1 ( 1+ i ) (Compounding factor)
t
o where i is the incentive and t are the future dates
o we want R1 today to be valued in the future(t)at R1 plus incentive(i) for delaying
consumption
General Equation: FV =PV (1+i )t where…
o FV = Future Value (growth on investment)
o PV = Present Value – the current value of your investment
o ( 1+i )t = Compounding Factor
If you are frequently compounding: FV =PV 1+ ( ) i tn
n
o Geometric Equation as n increases, there would be an upward sloping
function (exponential function)
o
EXPONENTIAL FUNCTION
, Economics-
202 -UKZN
FV
Present Value of Future Value: PV = where…
( 1+ i )t
1
is the discount factor
( 1+ i )t
What is the present value of a stream of Future Payments(f)?
PV = i 1−
f
[ 1
( 1+i )t ]
What do I invest today to earn a certain future payment(f) in perpetuity?
f
PV = where i is the current market interest rate.
i
Perpetuity means no maturity date/forever
Hence how much do I invest presently to earn the planned future payments
forever given the current market interest rate?
And f is the stream of future payments
Can you notice the
difference between the
two equations? What
has changed
202- UKZN
Investments
People value their present consumption more than their future consumption hence people
need incentives to delay their consumption.
People would prefer to have their money today grown by X amount to incentivize the
delay in consumption. This is because of positive time preferences.
1 ( 1+ i ) (Compounding factor)
t
o where i is the incentive and t are the future dates
o we want R1 today to be valued in the future(t)at R1 plus incentive(i) for delaying
consumption
General Equation: FV =PV (1+i )t where…
o FV = Future Value (growth on investment)
o PV = Present Value – the current value of your investment
o ( 1+i )t = Compounding Factor
If you are frequently compounding: FV =PV 1+ ( ) i tn
n
o Geometric Equation as n increases, there would be an upward sloping
function (exponential function)
o
EXPONENTIAL FUNCTION
, Economics-
202 -UKZN
FV
Present Value of Future Value: PV = where…
( 1+ i )t
1
is the discount factor
( 1+ i )t
What is the present value of a stream of Future Payments(f)?
PV = i 1−
f
[ 1
( 1+i )t ]
What do I invest today to earn a certain future payment(f) in perpetuity?
f
PV = where i is the current market interest rate.
i
Perpetuity means no maturity date/forever
Hence how much do I invest presently to earn the planned future payments
forever given the current market interest rate?
And f is the stream of future payments
Can you notice the
difference between the
two equations? What
has changed
