Business Mathematics and Basic Statistics · Ch 2 — Compound Interest
Compound Interest — The Idea of Interest on Interest
Compound Interest — The Idea of Interest on Interest
In simple interest, interest is calculated only on the original principal for every period of the loan or investment. In compound interest (CI), the interest earned at the end of each compounding period is added back to the principal, and the next period's interest is calculated on this larger amount. This is why compound interest is often described as interest on interest — money grows faster under compounding than under simple interest, and the gap widens as the number of periods increases.
This chapter, part of the WBCHSE Class 11 Commerce Business Mathematics and Basic Statistics syllabus, covers the compound-interest formula for four compounding frequencies — yearly, half-yearly, quarterly and monthly — worked strictly within the syllabus's own scope cap: every problem in this chapter uses a time span of at most 3 years.
Key Notation
Throughout this chapter: = principal (the sum originally invested or borrowed), = the annual (nominal) rate of interest, quoted as a percentage per year, = time in years, = the amount (principal + compound interest) at the end of the period, and .
Unlike simple interest, where the amount grows linearly with time (), compound interest grows geometrically — the amount at the end of one period becomes the principal for the next. This single idea, repeated compounding period after compounding period, is what the formulas in the rest of this chapter make precise.
The original sum of money invested or borrowed, before any compound interest is added to it.
The total value of an investment or loan after compound interest has been added — principal plus compound interest, .
The fixed interval — a year, a half-year, a quarter, or a month — at the end of which interest is calculated and added to the principal, so that the next period's interest is calculated on the larger, updated amount.
The stated yearly interest rate , before accounting for how many times a year it is actually compounded; the effective growth over a year is higher than once compounding happens more than once a year.