Math 1 · Unit 8
Compound Interest
Five lessons: simple interest (the line in money), compound interest (interest on interest), compounding more often, which account wins, and when money shrinks. Simple interest adds the same dollars every year; compound interest multiplies by the same factor every year, and every factor is 1 plus or minus the rate.
Simple Interest, the Line in Money
The words (principal, interest, rate, balance), then simple interest: I = Prt and A = P + Prt. The balance adds the same dollars every year, a constant difference, so it is a line with y-intercept P and slope Pr. Solve the formula for any letter with the Unit 1 moves.
Start Unit 8, Lesson 1Compound Interest, Interest on Interest
Interest on interest. The dollars earned grow every year, so compound interest is not a line. Adding 5% is multiplying by 1.05, so after t years the balance is P(1 + r) to the t: the Unit 7 exponential with P as the starting value and 1 + r as the growth factor. Read P and r out of an expression, and see why the balance is never 0.
Start Unit 8, Lesson 2Compounding More Often
Quarterly, monthly, daily. The yearly rate is split into n pieces: rate per period r over n, number of periods n times t. Read the parentheses as the growth factor for one period and the exponent as how many periods have passed. More often earns a little more, but only a little.
Start Unit 8, Lesson 3Which Account Wins?
Kevin earns $5 a month, Joseph earns 3% a month. Kevin leads for two and a half years, then Joseph passes him for good. City Bank at 3% simple beats National Bank at 2.6% compounded monthly for 10 years, then loses. A quantity that multiplies always passes one that adds, so the better account depends on how long you wait.
Start Unit 8, Lesson 4When Money Shrinks, and Using the Models
Depreciation: a car worth 35,000(0.87) to the t loses 13% a year, because 0.87 is 1 minus 0.13. A factor of 0.85 means losing 15%, not 85%. Debt grows by compound interest too. Then use the models: change the start or the rate, and answer how-long questions with a table. 72 divided by the rate estimates the doubling time.
Start Unit 8, Lesson 5Printables for Unit 8
Study guides, worksheets with answer keys, and lesson plans for every lesson in this unit.