Future Value

Study guide: Exam FM-2

The future value (FV) of a cash flow is its Accumulated Value at a specified future date, accounting for the time value of money. Under Compound Interest at effective annual rate i:

\text{FV} = \text{PV} \cdot (1+i)^n

• n is the number of periods.
• Future value is the inverse operation of Present Value: discounting finds PV from FV, while accumulation finds FV from PV.
• For a series of cash flows C_t at times t = 0, 1, \ldots, n, the future value at time n is:

\text{FV}_n = \sum_{t=0}^{n} C_t (1+i)^{n-t}

Saving for a Future Goal An investor deposits 500 at the start of each year for 4 years at 6% effective annual interest. Find the accumulated value at the end of year 4.

Answer This is an Annuity Due with payments of 500:

\begin{align*}
\text{FV} &= 500(1.06)^4 + 500(1.06)^3 + 500(1.06)^2 + 500(1.06)^1 \\
&= 500 \cdot \ddot{s}_{\overline{4}|0.06} \\
&= 500 \times 4.63709 \\
&\approx 2318.55
\end{align*}