for borrowing or lending money, most
often based on a percentage of the
requested amount. The two most com-
mon types of interest are simple and
compound. (For more information on
interest, see “Everyday Math.”)
In terms of a savings account, the
interest is usually compounded, which
means that any interest earned is rein-
vested, or compounded, to generate even
more money, and thus increase future
interest. Take, for example, a person start-
ing with $1,000 in a money market fund
earning 5 percent per year with quarterly
interest payments (or the person gets 5
percent divided by four, or 1.25 percent
per quarter). After one year, the $1,000
has grown to $1,050.95, making the com-
pound interest rate actually 5.095 per-
cent—not 5.00 percent—because interest
was also paid on the accumulated interest for each quarter. (An interest of 5 percent
only is called the simple interest rate; but most banking institutions pay compound
interest on savings.)
Simple and compound interest are both used in borrowing and lending. With sim-
ple interest, the interest is paid strictly on the amount of the initial principal (original
amount borrowed or lent), which is usually represented by the formula: a(t) a(0) (1
rt), in which a(t) is the sum of the principal and interest at the time tfor a constant
interest rate r.
Compound interest has a more complex formula. This type of interest is calculat-
ed not only on the initial principal, but also the interest accumulated (or accrued)
over time. For example, a person purchases a home for $250,000 and pays $50,000 as a
down payment. The remaining $200,000 is taken out as a loan at 8 percent interest for
30 years (compounded monthly) with equal monthly payments. The monthly mort-
gage payment (M), in which P is the principal, i is the interest rate, n is the number of
years, and q is the number of pay periods per year, would be:
M Pi / [q (1 [1 (i/q) ]nq)]
($200,000)(0.08) / [(12)(1 [1 (0.08/12)](30)(12)]
($1333.333333 ...)/(1 [1.006666666 ...]^360 )
$1,467.53 per month 389MATH IN THE HUMANITIES
In 2000 the Euro was formally introduced as the
preferred currency for members of the European
Economic Community. This greatly simplified trade
between these countries, which no longer had to
worry about converting currencies at rates that
could change daily. Photographer’s Choice.