Math 1 · Unit 8 · Lesson 3 · part 3 of 4

One example, all the way through

$1,000 at 6% for 1 year, four ways.

One example, all the way through

$1,000 at 6% for 1 year, four ways. The order matters, on paper and on the calculator: divide r by n, add 1, raise to the nt power, then multiply by P.

Monthly, step by step

1. Rate per period: 0.0612 = 0.005.

2. Add 1: the growth factor each month is 1.005.

3. Number of periods: 12 × 1 = 12. Power: 1.005¹² = 1.0616778.

4. Times P: 1000 × 1.0616778 = $1,061.68.

Calculator keys

0.06, divide, 12, equals. Plus, 1, equals. Power key, 12, equals. Times, 1000, equals.

If your calculator has parentheses, you can type it in one line: 1000 × ( 1 + 0.06 ÷ 12 ), power key, 12, equals.

Do not round in the middle. Round to the cent only at the end.

compounded	n	rate per period	periods	balance after 1 year
annually	1	0.061 = 0.06	1	$1,060.00
quarterly	4	0.064 = 0.015	4	$1,061.36
monthly	12	0.0612 = 0.005	12	$1,061.68
daily	365	0.06365	365	about $1,061.83

More often earns a little more, but only a little. Interest that is added sooner starts earning interest sooner, so monthly beats annual. But going from annual to monthly gained $1.68, and going all the way to daily gained only 15 cents more. The rate and the time matter far more than how often the bank compounds.

Try your own numbers. The comparer fills in every piece of the formula for the four common compounding periods.

Where to go next

Next: Practice ProblemsTry them, get help one step at a time, then print how it went. All the partsCompounding More Often