Continuous Compounding Compound Interest Explained The Power of

Continuous Compounding Compound Interest Explained The Power of Compounding 1

WARM - UP 1. Joey invests $4, 500 in an account that pays 1. 5% annual interest, compounded quarterly. What is his balance, to the nearest cent, at the end of 10 years? 1. How much more does $1, 000 earn in nine years, compounded daily at 4%, than $1, 000 over nine years at 4%, compounded semiannually? 2

Continuous Compounding Vocabulary CONTINUOUS COMPOUNDING: A method of calculating interest so that it is compounded an infinite number of times each year rather than being compounded every minute, or every microsecond. EXPONENTIAL BASE (e): The exponential base e is an irrational number which is a non-terminating, non-repeating decimal with an approximate value of e ≈ 2. 71828. . 3

Continuous Compounding interest daily makes money grow more quickly than simple interest. It is possible to compound interest every hour, every minute, even every second! 4

Continuous Compounding Continuously Compounded Interest is a great thing when you are earning it! Continuously compounded interest means that your principal is constantly earning interest and the interest keeps earning on the interest earned. 5

Continuous Compound Interest Formula B = pert where 6 B = ending balance p = principal e = exponential base r = interest rate expressed as decimal t = number of years Financial Algebra © Cengage Learning/South-Western

EXAMPLE 1 If you deposit $1, 000 at 4. 3% interest, compounded continuously, what would your ending balance be to the nearest cent after five years? 7 Financial Algebra © Cengage Learning/South-Western

EXAMPLE 2 Craig deposits $5, 000 at 5. 12% interest, compounded continuouslyfor four years. What would his ending balance be to the nearest cent? 8 Financial Algebra © Cengage Learning/South-Western

EXAMPLE 3 Patti wants to deposit $1, 000 and keep that money in the bank without deposits or withdrawals for eight years. She compares two different options. Option 1 will pay 2. 7% interest, compounded quarterly. Option 2 will pay 2. 4% interest, compounded continuously. a. How much interest does Option 1 pay? b. How much interest does Option 2 pay? 9 Financial Algebra © Cengage Learning/South-Western

PRACTIC E Pg. 154 #4 -10 10 Financial Algebra © Cengage Learning/South-Western