Algebra 2 · Unit 6 · Topic 6.3
Compound Interest and Growth Factors
With principal P, annual nominal rate r as a decimal, n compounding periods per year, and time t in years, the standard compound-interest model is A = P(1 + r/n)^(nt), assuming no transactions and a constant rate.
Definition and explanation
With principal P, annual nominal rate r as a decimal, n compounding periods per year, and time t in years, the standard compound-interest model is A = P(1 + r/n)^(nt), assuming no transactions and a constant rate.
Worked example
For P = $800, r = 0.06, n = 2, and t = 1, A = 800(1.03)² = $848.72. Each half-year uses a 3% rate, and there are two compounding periods in the year.
Common mistake
A quoted annual rate is not the rate for every compounding period; the rate and period count must agree.
Key takeaway
With principal P, annual nominal rate r as a decimal, n compounding periods per year, and time t in years, the standard compound-interest model is A = P(1 + r/n)^(nt), assuming no transactions and a constant rate.
Explain each step of the worked example, then check the units, signs, and conditions that apply.
Further reading
Topic coverage was checked against the openly available OpenStax Intermediate Algebra 2e, Algebra and Trigonometry 2e, and Introductory Statistics 2e textbooks. The explanations and examples on this site are independently written; textbook prose, exercises, and artwork are not reproduced.