3/9/12 Section 3.6/3.2 Obj: SWBAT solve real world applications using exponential growth and decay functions. Bell Ringer: Get Compound Interest Packet Part 2 HW Requests: pg 296 # 1-16 (3’s) 15, 32, 33 pg 342 #1-9 odds Homework: pg (3’s), 47, 50, 53, 55 Announcements: Tuesday -Quiz Log and Exponential Equations, Exponential Growth and Decay

Function for compound interest, compounding continuously: P = the principal amount r = the interest rate t = the number of years

Problem One thousand dollars is invested at 5% interest compounded continuously. a.Give the formula for A(t), the compounded amount after t years. b.How much will be in the account after 6 years? c.How long is required to double the initial investment?

(0.5)(12)

Calculator An annuity is a sequence of equal periodic payments. We will be working with ordinary annuities. The deposits are made at the end of each period and at the same time the interest is posted or added to the account.

How much interest will Genae pay in total?

How much interest will Genae pay? First how much is she paying total? $ * 60 = $40, Interest Paid: $40, $35000 = $

Compound Interest Compound interest is calculated each period on the original principal and all interest accumulated during past periods. Although the interest may be stated as a yearly rate, the compounding periods can be yearly, semiannually, quarterly, or even continuously. Simple Interest Simple interest is calculated on the original principal only. Accumulated interest from prior periods is not used in calculations for the following periods. Simple interest is normally used for a single period of less than a year, such as 30 or 60 days. where: Simple Interest I = P*r*n p = principal (original amount borrowed or loaned) i = interest rate for one period n = number of periods

Compound Interest Compound interest is calculated each period on the original principal and all interest accumulated during past periods. Although the interest may be stated as a yearly rate, the compounding periods can be yearly, semiannually, quarterly, or even continuously. Type of InterestPrincipal Plus Interest Earned Simple46, Compounded Yearly299, Compounded Quarterly347, The power of compounding can have an astonishing effect on the accumulation of wealth. This table shows the results of making a one-time investment of $10,000 for 30 years using 12% simple interest, and 12% interest compounded yearly and quarterly.

10) The Fresh and Green Company has a savings plan for employees. If an employee makes an initial deposit of $1000, the company pays 8% interest compounded quarterly. If an employee withdraws the money after five years, how much is in the account? 11) Using the information in the question above, find the interest earned if the money is withdrawn after 35 years. 12) Determine the amount of interest earned if $500 is invested at an interest rate of 4.25% compounded quarterly for 12 years.

10) The Fresh and Green Company has a savings plan for employees. If an employee makes an initial deposit of $1000, the company pays 8% interest compounded quarterly. If an employee withdraws the money after five years, how much is in the account? A = $ ) Using the information in the question above, find the interest earned. Simple Interest Compound Interest 12) Determine the amount of interest earned if $500 is invested at an interest rate of 4.25% compounded quarterly for 12 years.

10) The Fresh and Green Company has a savings plan for employees. If an employee makes an initial deposit of $1000, the company pays 8% interest compounded quarterly. If an employee withdraws the money after five years, how much is in the account? A = $ ) Using the information in the question above, find the interest earned. Simple Interest I = prt I = 1000*.08* 5 = $400 Compound Interest = $ $1000 = $ ) Determine the amount of interest earned if $500 is invested at an interest rate of 4.25% compounded quarterly for 12 years. Simple Interest Compound Interest

10) The Fresh and Green Company has a savings plan for employees. If an employee makes an initial deposit of $1000, the company pays 8% interest compounded quarterly. If an employee withdraws the money after five years, how much is in the account? A = $ ) Using the information in the question above, find the interest earned. Simple Interest I = prt I = 1000*.08* 5 = $400 Compound Interest = $ $1000 = $ ) Determine the amount of interest earned if $500 is invested at an interest rate of 4.25% compounded quarterly for 12 years. Simple Interest $255 Compound Interest $830.41