TERMINOLOGY, TIMELINES, AND TABLES
An
interest rate is a rate of return provided on invested funds and usually paid in
cash. When the interest rate is
used to calculate future values dollar amounts the interest rate is often
referred to as a compound interest rate. In
most financial mathematical calculations, interest rates are considered to be
compound interest rates even if the “compound” term is not used.
Compound interest rate factors are usually referred to as Future Value Interest Factors (FVIF) although some textbooks use the term Compound Value Interest Factors (CVIF). Both terms refer to the same concept.
Discount Rate
A
discount rate is an interest rate (or rate of return) that is used when calculating present values
from future dollar amounts. A
discount rate is, essentially, the inverse of a compound interest rate or
compound rate of return.
Discount
rate factors are referred to as Present Value Interest Factors (PVIF).
PVIF’s values are the exact inverse of the FVIF’s for the same
percentage interest rate and number of periods.
This
general concept of discount rates used in TVM calculations should not be confused with the Federal
Reserve Discount Rate or a Bond’s Discount from Par value.
Simple
interest calculations refer to a type of interest calculation in which interest
earnings are calculated only on the principal (original) amount of the investment. If the
sum of money is invested for multiple years, interest is a only paid of the
original principal amount invested. Interest
is not calculated and paid on interest earnings that were paid in earlier
periods. Simple interest calculations are not the type of calculations performed
in time value of money problems.
Compound Interest
Compound
interest calculations refer to a type of interest calculation in which interest
earnings are calculated not only on the principal (original)
amount of the investment, but also on past interest earnings that are assumed to
have been reinvested at the same rate. If the
sum of money is invested for multiple years, interest paid is reinvested and
future interest payments reflect interest earned on both the principal and the
past interest earned. Compound interest calculations are the type of
calculations performed in time value of money problems.
Future Values
Dollar amounts to be paid or received at some point in the future.
Present Values
Dollar amounts to be paid or received today.
Annuity
Stream of equal dollar amount payments made over time.
Ordinary Annuity
Stream of equal dollar amount payments where payments are made at the end of each period for a certain number of periods
Annuity Due
Stream of equal dollar amount payments where payments are made at the beginning of each period for a certain number of periods.
Section II - Timelines
Timelines are graphic representations of patterns of cash flows over time. They are a great help for students who are learning basic time value of money calculations. They can also be used to model more complex patterns of cash flows for more complicated financial problems. I strongly recommend you draw a timeline for every TVM problem you solve.
Section III - Tables
Time value of money tables present the interest rate factors associated with different TVM calculations and combinations of interest (or discounts) rates and number of compounding (or discounting) periods. There are four basic tables that correspond to the four basic types of TVM calculations;
Present Value Interest Factors (PVIF) for taking future dollar amounts and restating as present values.
Future Value Interest Factors (FVIF) for taking present value dollar amounts and restating as future values.
Present Value Interest Factors for Annuities (PVIFA) for calculating a single present value of an annuity stream.
Future Value Interest Factors for Annuities (FVIFA) for calculating a single future value of an annuity stream.
Every introductory finance text has some version of these four basic tables. the two annuity tables (PVIFA and FVIFA) are tables that are designed for "ordinary annuities" in which payments are made at the end of each period. Tables are not usually published for "annuity due" tables since the required interest rate factors can be easily calculated from the ordinary annuity tables. See the assigned text for examples of TVM interest rate factor tables.