3 5 COMPOUND INTEREST Your money can grow

WARM - UP 1. Josh has a savings account at a bank that charges

Vocabulary CREDITING: The bank pays interest every single day, based on that day’s principal,

Vocabulary ANNUAL PERCENTAGE YIELD (APY): The APY is the annual interest rate it would

Compounding # times per year This is every ____ Annual Semiannual Quarterly Monthly Daily

EXAMPLE 1 Marie deposits $1, 650 for three years at 3% interest, compounded daily.

EXAMPLE 2 Kate deposits $2, 350 in an account that earns interest at a

EXAMPLE 3 Write an algebraic expression for the ending balance after k years of

EXAMPLE 4 Barbara deposits $3, 000 in a one year CD at 4. 1%

EXAMPLE 5 Spencer deposits $10, 000 in a two year CD at 1. 9%

PRACTICE Page 148, # 2 -4, 8, 12, 14, 16 18 Financial Algebra ©

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3 -5 COMPOUND INTEREST Your money can grow larger and quicker with compound interest than it can with simple interest. 1

WARM - UP 1. Josh has a savings account at a bank that charges a $10 fee for every month his balance falls below$1, 000. His account has a balance of $1, 203. 44 and he withdraws $300. What will his balance be in six months if he makes no deposits or withdrawals? 2. Laura deposits $2, 000 in an account that has an annual interest rate of 3. 96%. How much simple interest will she earn at the end of 3½ years? 2

Simple v. Compound Investopedia Video 3

Introduction 4

Vocabulary CREDITING: The bank pays interest every single day, based on that day’s principal, but does not add the interest every day. Instead, they keep a record of interest earned and add it into the account monthly or quarterly. Most common procedure in banks today is compounding daily and crediting monthly. $ $ $ ANNUAL PERCENTAGE RATE (APR): The interest rate paid per year or charged per year. This does not include compounding within the year! Sometimes this will include non-interest charges and fees. 5

Vocabulary ANNUAL PERCENTAGE YIELD (APY): The APY is the annual interest rate it would take to give the same dollar amount of interest that the compounding gave. Includes the money earned off of interest. $ $ $ COMPOUND INTEREST: With compound interest, the account earns interest on the interest, so the principal plus any earned interest is used to calculate the interest. Each time interest is calculated the principal is slightly higher than the previous time because of the added interest 6

Compounding # times per year This is every ____ Annual Semiannual Quarterly Monthly Daily 7

Compound Interest Formula 8

EXAMPLE 1 Marie deposits $1, 650 for three years at 3% interest, compounded daily. What is her ending balance? 9 Financial Algebra © Cengage Learning/South-Western

EXAMPLE 2 Kate deposits $2, 350 in an account that earns interest at a rate of 3. 1%, compounded monthly. What is her ending balance after five years? Round to the nearest cent. 10 Financial Algebra © Cengage Learning/South-Western

EXAMPLE 3 Write an algebraic expression for the ending balance after k years of an account that starts with a balance of $2, 000 and earns interest at a rate of 3. 5%, compounded daily. 11 Financial Algebra © Cengage Learning/South-Western

Office Space 12

Office Space (part 2) 13

Annual Percentage Yield 14

APR v. APY Video 15

EXAMPLE 4 Barbara deposits $3, 000 in a one year CD at 4. 1% interest, compounded daily. What is the annual percentage yield (APY) to the nearest hundredth of a percent? 16 Financial Algebra © Cengage Learning/South-Western

EXAMPLE 5 Spencer deposits $10, 000 in a two year CD at 1. 9% interest, compounded monthly. What is Spencer’s APY to the nearest hundredth of a percent? 17 Financial Algebra © Cengage Learning/South-Western