Math 1 · Unit 8 · Lesson 3 · part 2 of 4
Splitting the year into periods
In Lesson 2 the bank added interest once a year.
Splitting the year into periods
In Lesson 2 the bank added interest once a year. Many banks add it more often. The time between additions is the compounding period.
Compounded annually1 time a year. n = 1.
Compounded quarterly4 times a year, every 3 months. n = 4.
Compounded monthly12 times a year. n = 12.
Compounded daily365 times a year. n = 365.
The bank does not pay the whole yearly rate each time. It splits the yearly rate into n equal pieces and pays one piece each period. Two things change from Lesson 2:
- 1The rate per period is rn.The yearly rate divided by the number of periods in a year. 6% a year paid monthly is 0.0612 = 0.005 each month, which is half a percent.
- 2The number of periods is n times t.n periods every year, for t years. Monthly for 5 years is 12 × 5 = 60 periods.
Put those two into Lesson 2's formula, growth factor to the number of times you multiply:
A = P(1 + rn)nt
Read the pieces as whole quantitiesDo not read this letter by letter. Read it in chunks. The parentheses, 1 + rn, are the growth factor for one period: keep all of it, plus one piece of the yearly rate. The exponent, nt, is how many periods have passed, how many times the account has been multiplied. P is still the starting value. It is the same sentence as Lesson 2: start with P, multiply by the growth factor once for every period.
When n = 1, rn is just r and nt is just t, so this is Lesson 2's formula again. Nothing was thrown away.