84 CHAPTER 2 Time Value of Money1.Nominal, or quoted, rate.^10 This is the rate that is quoted by banks, brokers, and
other financial institutions. So, if you talk with a banker, broker, mortgage lender,
auto finance company, or student loan officer about rates, the nominal rate is the one
he or she will normally quote you. However, to be meaningful, the quoted nominal
rate must also include the number of compounding periods per year. For example, a
bank might offer 6 percent, compounded quarterly, on CDs, or a mutual fund might
offer 5 percent, compounded monthly, on its money market account.
The nominal rate on loans to consumers is also called the Annual Percentage
Rate (APR).For example, if a credit card issuer quotes an annual rate of 18
percent, this is the APR.
Note that the nominal rate is never shown on a time line, and it is never used as an input
in a financial calculator, unless compounding occurs only once a year.If more frequent com-
pounding occurs, you should use the periodic rate as discussed below.
2.Periodic rate, iPER.This is the rate charged by a lender or paid by a borrower
each period. It can be a rate per year, per six-month period, per quarter, per
month, per day, or per any other time interval. For example, a bank might charge
1.5 percent per month on its credit card loans, or a finance company might
charge 3 percent per quarter on installment loans. We find the periodic rate as
follows:
Periodic rate, iPERiNom/m, (2-10)
which implies that
Nominal annual rate iNom(Periodic rate)(m). (2-11)
Here iNomis the nominal annual rate and m is the number of compounding pe-
riods per year. To illustrate, consider a finance company loan at 3 percent per
quarter:
Nominal annual rate iNom(Periodic rate)(m) (3%)(4) 12%,
or
Periodic rate iNom/m 12%/4 3% per quarter.
If there is only one payment per year, or if interest is added only once a year, then
m 1, and the periodic rate is equal to the nominal rate.
The periodic rate is the rate that is generally shown on time lines and used in calcu-
lations.^11 To illustrate use of the periodic rate, suppose you invest $100 in an(^10) The term nominal rateas it is used here has a different meaning than the way it was used in Chapter 1.
There, nominal interest rates referred to stated market rates as opposed to real (zero inflation) rates. In this
chapter, the term nominal ratemeans the stated, or quoted, annual rate as opposed to the effective annual
rate, which we explain later. In both cases, though, nominalmeans stated,or quoted,as opposed to some ad-
justed rate.
(^11) The only exception is in situations where (1) annuities are involved and (2) the payment periods do not
correspond to the compounding periods. If an annuity is involved and if its payment periods do not corre-
spond to the compounding periods—for example, if you are making quarterly payments into a bank account
to build up a specified future sum, but the bank pays interest on a daily basis—then the calculations are more
complicated. For such problems, one can proceed in two alternative ways. (1) Determine the periodic (daily)
interest rate by dividing the nominal rate by 360 (or 365 if the bank uses a 365-day year), then compound
each payment over the exact number of days from the payment date to the terminal point, and then sum the
compounded payments to find the future value of the annuity. This is what would generally be done in the
real world, because with a computer, it would be a simple process. (2) Calculate the EAR, as defined on the
next page, based on daily compounding, then find the corresponding nominal rate based on quarterly com-
pounding (because the annuity payments are made quarterly), then find the quarterly periodic rate, and
then use that rate with standard annuity procedures. The second procedure is faster with a calculator, but
hard to explain and generally not used in practice given the ready availability of computers.