Financial Algebra© Cengage Learning/South-Western

Warm-UpWarm-UpWarm-UpWarm-Up

Grab a paper from the backSusan wants to invest her $1,500 into a savings

account that compounds quarterly. The account offers an 8% annual interest rate.How much money did she have after the first 3 months?How much money did she have after six months?How much money did she have after nine monthsHow much money did she have at the end of the year?

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Financial Algebra© Cengage/South-Western Slide 22

3-5

COMPOUND INTEREST FORMULA

3-5

COMPOUND INTEREST FORMULA

Become familiar with the derivation of the compound interest formula.

Make computations using the compound interest formula.

OBJECTIVES

Financial Algebra© Cengage Learning/South-Western Slide 33

compound interest formula annual percentage rate (APR) annual percentage yield (APY)

Key Terms

Financial Algebra© Cengage Learning/South-Western Slide 44

What are the advantages of using What are the advantages of using the compound interest formula?the compound interest formula?What are the advantages of using What are the advantages of using the compound interest formula?the compound interest formula?

How did the use of computers make it easier for banks to calculate compound interest for each account?

Without the help of computers, how long do you think it would take you to calculate the compound interest for an account for a five year period?

Financial Algebra© Cengage Learning/South-Western

Compound InterestCompound InterestCompound InterestCompound Interest

Obviously, using the simple interest formula to compute compound interest is tedious

Luckily, by the powers of Mathematics, there is a formula that has been created which makes this much easier

The compound interest formula relates principal, the interest rate, number of compounds in a year, the number of total year, and the ending balance

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Financial Algebra© Cengage Learning/South-Western

Compound InterestCompound InterestCompound InterestCompound Interest

The annual interest rate a bank offers is called the Annual Percentage Rate (APR)

Most banks advertise the Annual Percentage Yield, (APY)The bank takes the dollar amount of interest you earn under

the compounding to create the APY. The APY is the simple interest rate that would be required to give the same dollar amount of interest that the compounding gave.Therefore, annual percentage yield (APY) is an annual rate of

interest that takes into account the effect of compounding.

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Financial Algebra© Cengage Learning/South-Western

Annual Percentage Yield (APY)Annual Percentage Yield (APY)Annual Percentage Yield (APY)Annual Percentage Yield (APY)

Annual Percentage Yield (APY)The bank takes the dollar amount of interest you

earn under the compounding to create the APY. The APY is the simple interest rate that would be required to give the same dollar amount of interest that the compounding gave. Therefore, annual percentage yield (APY) is an annual rate of interest that takes into account the effect of compounding.

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Financial Algebra© Cengage Learning/South-Western

Compound Interest FormulaCompound Interest FormulaCompound Interest FormulaCompound Interest Formula

A = P (1 + ) nt

A = Ending balanceP = principal (original balance)r = interest rate expressed as decimaln = number of times interest is compounded annually

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Financial Algebra© Cengage Learning/South-Western

Compound Interest FormulaCompound Interest FormulaCompound Interest FormulaCompound Interest Formula

A = P (1 + ) nt

THIS FORMULA NOW GIVES US OUR “ENDING

BALANCE” – NOT JUST OUR INTEREST MADE

TO FIND THE INTEREST MADE, WE WOULD HAVE TO

DO A - P

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Nancy deposits $1,200 into an account that pays 3% interest, compounded monthly. What is her ending balance after one year? Round to the nearest cent.

CHECK YOUR UNDERSTANDING

Financial Algebra© Cengage Learning/South-Western Slide 1111

B = p(1 + )nt

B = ending balance p = principal or original balancer = interest rate expressed as a decimaln = number of times interest is compounded annuallyt = number of years

rn

Compound Interest FormulaCompound Interest FormulaCompound Interest FormulaCompound Interest Formula

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EXAMPLE 3EXAMPLE 3EXAMPLE 3EXAMPLE 3

Marie deposits $1,650 for three years at 3% interest, compounded daily. What is her ending balance?

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EXAMPLE 4EXAMPLE 4EXAMPLE 4EXAMPLE 4

Sharon deposits $8,000 in a one year CD at 3.2% interest, compounded daily. What is Sharon’s annual percentage yield (APY) to the nearest hundredth of a percent?