Interest and the Basic Terms

When a sum of money is lent by one person (the lender) to another (the borrower), the borrower pays an extra charge for the use of that money over and above the amount actually borrowed. This extra charge is called interest. The Odisha CHSE Std-11 Business Mathematics and Statistics syllabus treats interest as an application of the same commercial-arithmetic principles used throughout banking, trade and finance, applied here to loans, deposits and investments.

Five quantities occur again and again in every interest problem, and getting comfortable with their symbols and units is the whole foundation of this chapter:

• Principal ($P$) — the original sum of money borrowed, lent or invested. Also called the sum or the capital.
• Rate of interest ($R$) — the interest charged on ₹100 for one unit of time (usually one year). It is stated as a percentage per annum, written R% p.a. ("per annum" means "per year").
• Time ($T$ or $n$) — the period for which the money is borrowed or invested, normally measured in years.
• Interest ($I$) — the total charge paid for the use of the principal over the whole time period.
• Amount ($A$) — the total sum the borrower finally repays, i.e. the principal plus the interest: $A = P + I$

There are two distinct ways of charging interest, and the entire chapter turns on the difference between them:

1. Simple interest, where interest is charged only on the original principal for the whole period (§2–§3).
2. Compound interest, where interest is periodically added to the principal so that the next period's interest is charged on the grown amount — interest earning interest (§4–§6).

Because both methods use the same five quantities, keeping the units consistent is essential: the rate and the time must refer to the same unit of time. A rate quoted "per annum" must go with a time measured in years; if interest is compounded more often than once a year, both the rate and the number of periods have to be adjusted to match (§6).