The Idea of Present Value

• Present value: what principal should I invest to obtain $X t years from now?
  • Effectively a way to travel back in time when starting with a future value

• The above equation is the generalized case, though we will almost always encounter compound interest, in which $a(t)$ has the form $(1 + i)^t$
  • Therefore, for compound interest: $A_0 = A(t)(1 + i)^{-t}$
  • $\nu=(1+i)^{-1}$ is known as the discount factor and it is the inverse of the accumulation factor
• A discount function relates the value needed to invest today to obtain a particular amount in the future; it is equal to $[a(t)]^{-1}=\frac{1}{(1+i)^t}=\nu^t$ (only for compound interest, though the concept is similar for simple interest)
• Discounting and accumulation are opposite processes
  • Discounting goes backwards in time from the final value to get the present value
  • Accumulation goes forward in time from the present value to get the final value