Page 425 - Encyclopedia of Business and Finance

eobf_I 7/5/06 3:04 PM Page 402

Interest Rates

Effect of changing interest rates on the Effect of changing interest rates on the value
amount of monthly payments of an investment in debt, holding n constant

Borrow $100,000 Borrow $20,000 $20,000 maturity value bonds $20,000 in treasury bills
for home purchase for auto purchase paying 8% (stated) annual paying 0% interest
interest, due in 25 years due in 90 days
Interest 30-Year Interest 4-Year
rate mortgage payment rate auto loan Market Market Market value
interest Market value interest of the
6% $599.55 7% $478.93 rate of the bonds rate treasury bills
8% $733.76 10% $507.25
6% $25,113 6% $19,711
8% $20,000 8% $19,619
10% $16,369 10% $19,529
Table 1
Table 2
The formula used to calculate the amount of interest
is:
annuity factor = a number obtained from an ordi-
interest = principal ¥ interest rate ¥ time [1]
nary annuity table that is determined by the
where: interest rate (i) and the number of annuity pay-
ments (n).
principal = amount of money borrowed
An analysis of the effect of changes in interest rates
interest rate = percent paid or earned per year
requires controlling (or holding constant) two of the other
time = number of years three variables in equation [3].
Equation [1] can be rewritten as: The term “future cash flow(s)” describes cash that
will be received in the future. Holding the number of pay-
interest rate = interest ÷ principal [2]
ments and the amount of each payment constant, the
where: present value of future cash flows is inversely related to the
interest rate. Holding the number of payments and pres-
time = one year
ent value of the future cash flows constant, the amount of
The principal is also known as the present value. The each payment is directly related to the interest rate. Hold-
interest rate in equation [2] is called the annual percent- ing the present value of the future cash flows and the
age rate or APR. APR is the most useful measure of inter- amount of each payment constant, the number of pay-
est rate. (In the remainder of this discussion, the term ments is directly related to the interest rate. In summary,
“interest rate” refers to the APR.) everything else held constant, increases in the interest rate
Equations [1] and [2] are useful in situations that (1) increase the amount of each payment, or (2) increase
involve only one cash flow (a single-payment scenario). the number of payments required, or (3) decrease the
Many economic transactions, however, involve multiple present value of the future cash flows.
cash flows. For instance, a consumer acquires a good or In order to understand the effect of changes in inter-
service and in exchange promises to make a series of pay- est rates from a consumer’s perspective, we first examine
ments to the supplier. This type of transaction describes borrowing transactions in which the present value of the
an annuity. An annuity is a series of equally spaced pay- future cash flows and the number of payments are fixed.
ments of equal amount. The annuity formula is: Consider, for instance, a thirty-year mortgage or a four-
year auto loan. In each case, the effect of an increase in
present value of annuity =
interest rates is an increase in the amount of the home or
annuity payment ¥ annuity factor i,n [3]
auto payment. This is shown in Table 1.
where: Well-known lending interest rates include the prime
rate, the discount rate, and consumer rates for automo-
present value of annuity = value of the good or serv- biles or mortgages. The discount rate is the rate that the
ice received today (when the exchange transac- Federal Reserve bank charges to banks and other financial
tion is finalized) institutions. This rate influences the rates these financial
annuity payment = amount of the payment that is institutions then charge to their customers. The prime rate
made each period is the rate banks and large commercial institutions charge

402 ENCYCLOPEDIA OF BUSINESS AND FINANCE, SECOND EDITION