**Time Value of Money: Using Present Value Factors**

**Introduction**

The time value of money equation is:

0 = PV + PMT * PVAF + FV * PVSF

where

PVAF = present value of annuity factor = Σ( (1 + i%)^(-k), k, 1, n )

PVSF = present value of single factor = (1 + i%)^-n

n = number of payments

i% = periodic interest rate (as a decimal)

The cash flow convention is maintained with this model. Cash outflows (payments) are negative, cash inflows (receipts) are positive.

**Solving for Payment (PMT)**

0 = PV + PMT * PVAF + FV * PVSF

-PMT * PVAF = PV + FV * PVSF

-PMT = (PV + FV * PVSF) / PVAF

PMT = -(PV + FV * PVSF) / PVAF

Example

PV = $50,000.00

FV = -$10,000.00

n = 60 (5 years of monthly payments)

i% = 0.05/12

PVAF = 52.99071

PVSF = 0.77921

PMT = -(50000 – 10000 * 0.77921) / 52.99071 = -796.5150873

(cash payment of $796.52)

**Solving for Future Value (FV)**

0 = PV + PMT * PVAF + FV * PVSF

-FV * PVSF = PV + PMT * PVAF

FV = -( PV + PMT * PVAF ) / PVSF

Example

PV = -$1,000.00

PMT = -$250.00

n = 60 (5 years of monthly payments)

i% = 0.05/12

PVAF = 52.99071

PVSF = 0.77921

FV = -( -1000 – 250 * 52.99071) / 0.77921 = 18284.7724

(future value of deposit $18,284.77)

We can use this method with any calculator. A partial present value factor table, one for single payment, and one for annuity, is presented below.

Source:

“HP 17BII Financial Calculator Owner’s Manual” Edition 1 Hewlett Packard. Corvallis, OR. December 1989.

Have fun,

Eddie

All original content copyright, © 2011-2019. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.