Growth & Discounting

Present Value

To compare values across time, we discount future cash to the present.

highlighted = computed this step

Present-value formula

Present value discounts future cash to today. PV is the future cash flow divided by one plus the period rate, raised to period count n=3.

$1,331.00/(1+10%)3=$1,000.00\$1,331.00/(1+10\%)^{3} = \$1,000.00
Present valueA future payment is worth less today. 0123$1,331.00PV: $1,000.00

Exact today value

Receiving $1,331.00 in 3 periods is worth $1,000.00 today at 10%.

PV(in 3 periods)=$1,000.00\text{PV}(\text{in }3\text{ periods}) = \$1,000.00
Present valueA future payment is worth less today. 0123$1,331.00PV: $1,000.00

Rounding note

The present-value setup is the inverse of the compound-interest thread for the same amount and rate: value moved forward and backward across periods returns to the same amount. Round-half-up to the cent is used for display. Institutions or regulations may use different rules (for example, banker's rounding or round-half-to-even).

PV3( periods)=$1,331.00(1+10100)3\text{PV}_{3}(\text{ periods}) = \frac{\$1,331.00}{(1+\frac{10}{100})^{3}}