Present & Future Value

Present & Future Value

The time value of money is the foundational principle of finance: a dollar today is worth more than a dollar in the future.

Future Value

If you invest $PV today at interest rate $r$ per period for $n$ periods:

$FV = PV \cdot (1 + r)^n$

Present Value

To find what a future amount is worth today (discounting):

$PV = \frac{FV}{(1 + r)^n}$

The factor $\frac{1}{(1+r)^n}$ is called the discount factor.

Example

Invest $1000 at 5% annually for 3 years:

• FV = 1000 × (1.05)³ = $1157.63

What is $1000 received in 3 years worth today at 5%?

• PV = 1000 / (1.05)³ = $863.84

Implement both functions using Python's ** exponentiation operator.