Math 1 · Unit 8 · Lesson 3
Compounding More Often
Banks often add interest more than once a year: quarterly, monthly, or daily. The yearly rate is split into n equal pieces, so the rate per period is r over n, and interest is added n times t times in all. Read the formula in chunks: the parentheses are the growth factor for one period, and the exponent is how many periods have passed. Compounding more often earns a little more, because interest starts earning interest sooner, but only a little.
The big idea
When interest is added more than once a year, the yearly rate is split into n equal pieces. The rate per period is r over n, and the number of periods is n times t, so the balance is P times (1 plus r over n) to the nt. Read it in chunks: the parentheses are the growth factor for one period, the exponent is how many periods have passed, and P is the starting value, which is the same sentence as Lesson 2 said once per period instead of once per year. Work it in order: divide r by n, add 1, raise to the nt power, then multiply by P, rounding only at the end. Compounding more often earns a little more, because interest starts earning interest sooner, but the gain is small: on $1,000 at 6% for a year, monthly beats annual by $1.68 and daily adds only 15 cents more.
The parts of this lesson
Each part is its own short page. Go in order, or pick the one you need.
Printables
One page with the four compounding periods, rate per period and number of periods, the formula read in chunks, the calculator order, and the $1,000 at 6% comparison. Plus a worksheet with an answer key and a short lesson plan.
Where this goes next
NC Math 1 standards in this lesson: NC.M1.A-SSE.1b (read a group of parts as one quantity), NC.M1.F-IF.8b (interpret growth rates), NC.M1.F-LE.5 (interpret the parameters in context).