Compound interest (capstone)
This lesson pulls together everything so far - percentages, order of
operations, and exponents - into one real formula: the one a bank actually
uses to grow a balance that earns interest more than once a year.
A = P * (1 + r/n)^(n*t)
A = the final amount
P = the principal (starting balance)
r = the annual interest rate, as a decimal
n = how many times per year it compounds
t = the number of years
Read it as a sentence: start with P, and for every one of the n * t
compounding periods, multiply by a little bit of growth (1 + r/n). The
exponent is doing the "apply this growth repeatedly" work.
The starter expression shows the shape with easy numbers ($100 at 10%,
compounded once, for one year) - swap in this lesson's real numbers.
Your task: $1000 principal, 5% annual interest rate, compounded monthly
(12 times a year), for 3 years. What's the final amount?
You'll practice:
- Reading a multi-variable formula and substituting real numbers directly
- Nesting parentheses correctly so the exponent applies to the whole growth factor
Related reading: How to Read Math Notation →