3-6 Continuous Compounding Compound Interest Explained The Power of Compounding JA Finance Park Saving, Investing, and Risk Management

WARM - UP 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? How much more does $1,000 earn in nine years, compounded daily at 4%, than $1,000 over nine years at 4%, compounded semiannually?

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 ≈ 2.718281828 . . . . JA Finance Park Saving, Investing, and Risk Management 3

3-6 Continuous Compounding Compounding interest daily makes money grow more quickly than simple interest. It is possible to compound interest every hour, every minute, even every second!

3-6 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.

Continuous Compound Interest Formula B = pert where B = ending balance p = principal e = exponential base r = interest rate expressed as decimal t = number of years

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

EXAMPLE 2 Craig deposits $5,000 at 5.12% interest, compounded continuously for four years. What would his ending balance be to the nearest cent? 8

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

PRACTICE Pg. 154 #4-10 10