Financial Algebra © Cengage Learning/South-Western Warm-UpWarm-Up Grab a paper from the back Susan 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 months How much money did she have at the end of the year? Slide 1

Financial Algebra © Cengage/South-Western Slide 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 3 compound interest formula annual percentage rate (APR) annual percentage yield (APY) Key Terms

Financial Algebra © Cengage Learning/South-Western Slide 4 What are the advantages of using 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 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 Slide 5

Financial Algebra © Cengage Learning/South-Western Compound 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. Slide 6

Financial Algebra © Cengage Learning/South-Western 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. Slide 7

Financial Algebra © Cengage Learning/South-Western Compound Interest Formula A = P (1 + ) nt A = Ending balance P = principal (original balance) r = interest rate expressed as decimal n = number of times interest is compounded annually Slide 8

Financial Algebra © Cengage Learning/South-Western Compound 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 Slide 9

Financial Algebra © Cengage Learning/South-Western Slide 10 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 11 B = p (1 + ) nt B = ending balance p = principal or original balance r = interest rate expressed as a decimal n = number of times interest is compounded annually t = number of years r n Compound Interest Formula

Financial Algebra © Cengage Learning/South-Western Slide 12 EXAMPLE 3 Marie deposits $1,650 for three years at 3% interest, compounded daily. What is her ending balance?

Financial Algebra © Cengage Learning/South-Western Slide 13 EXAMPLE 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?