Do Now These are the terms from yesterday. Please define(type answer) – Principal – Interest Rate – Time – Simple Interest earned These are the terms for today. Are you familiar with any of them? – Future Value – Present Value – Frequency of compounding 1

Do Now Please complete Part 1 of the Simple and Compound Interest Handout.

Standard 5.3 Students will understand the difference between earning simple and compound interest and will be able to calculate long term gains from savings. 3

Goals of the day: I can: understand the differences between earning simple and compound interest calculate the earnings from simple and compound interest understand the Rule of 72 (and calculate how long it will take to double my money using the Rule)

Please write down your answer Yesterday, we learned about simple interest and today we will learn about compound interest. Which method do you think will make you more money? Why? What is the relationship between interest rates and your overall return on your savings investment? 5

Compound Interest Compound Interest is calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan. Compound Interest can be thought of as “interest on interest” and will make a deposit or a loan grow at a faster rate than Simple Interest (which is interest calculated only on the principal amount.) 6

Compound Interest (Cont.) The rate at which compound interest accrues depends on the frequency of compounding; the higher the number of compounding periods, the greater the compound interest. Compounding Factors: – Annual - 1 – Semi-annual - 2 – Quarterly - 4 – Monthly - 12 – Daily

Frequency of Compounding As frequency of compounding Interest Income received at end of period 8

Calculate Compound Interest Formula: FV=PV(1+r/m)^m*t FV- Future Value PV-Present Value r-rate m-compounding factor t- time 9 Compounding Factors Annual- 1 Semi-annual- 2 Quarterly- 4 Monthly- 12 Daily- 365

Let’s Review Order of Operations PEMDAS(Please excuse my dear aunt sally) Parentheses, Exponents, Multiplication, Division, addition, subtraction Group activity(Groups of 5) In groups of 5 you will arrange the individual parts of the formula in the proper order of operations.

Calculate Compound Interest 11 #1 Together: Calculate Compound Interest on principal of $2, at 6% compounded annually for 10 years. Step 1: Identify the components of the problem: PV _______ r_________ m________ t _______________ Formula: FV=PV(1+r/m)^m*t

Calculate Compound Interest 12 #1 Together: calculate Compound Interest on principal of $2, at 6% compounded annually for 10 years. PV = $2,500 r = 6% m = 1 t = 10 Step 2: Create the formula here: 2500(1+(.06/1))^1*10 Step 3: Plug the numbers into your calculator and solve $________________________. Compound Interest Formula: FV=PV(1+r/m)^m*t Sample calculator keys: FV=PV(1+(r/m))^(m*t)

Remember to Round Your Answers to Dollars! Calculator Keys: 2500(1+(.06/1))  (1*10) 4, is rounded to $4,477.12

Calculate Compound Interest 14 #2 Together: calculate Compound Interest on principal of $5, at 8% compounded annually for 10 years. Step 1. Identify the components of the problem: PV_______ r_______ m_______ t_______ Step 2: Create the formula here: Step 3: Plug the numbers into your calculator and solve $________________________ (remember to round to $$’s) Compound Interest Formula: FV=PV(1+r/m)^m*t Sample calculator keys: FV=PV(1+(r/m))^(m*t)

Calculate Compound Interest 15 #1 On Your Own: Calculate Compound Interest on principal of $8, at 7% compounded monthly for 25 years. Step 1. Identify the components of the problem PV_______ r_______ m_______ t_______ Step 2: Create the formula here: Step 3: Plug the numbers into your calculator and solve $________________________ (remember to round to $$’s) Compound Interest Formula: FV=PV(1+r/m)^m*t Sample calculator keys: FV=PV(1+(r/m))^(m*t)

Calculate Compound Interest 16 #2 On Your Own: calculate Compound Interest on principal of $8, at 7% compounded monthly for 25 years. Step 1. Identify the components of the problem PV_______ r_______ m_______ t_______ Step 2: Create the formula here: Step 3: Plug the numbers into your calculator and solve $________________________ (remember to round to $$’s) Compound Interest Formula: FV=PV(1+r/m)^m*t Sample calculator keys: FV=PV(1+9r/m))^(m*t)

Calculating Interest Handout Please complete Part 2 of the Simple and Compound Interest Handout.

Calculating Interest Handout What did you discover about the around of interest you earned: 1.With Simple Interest compared to Compound Interest? 2.When you increased the frequency of compounding? 3.When you increased the interest rate?

Rule of 72 Quick way of finding out how long it will take to double your money! Rule was first mentioned in an arithmetic book published in Rule is: The number 72 divided by the interest rate The result is the number of years it will take to double your money 19

Rule of 72 (continued) Working Together: If you save $2,000 at a 8% interest rate, how many years will it take to grow into $4,000? Rule of 72 formula: 72/Interest Rate (expressed as a number) 72/8= 9 It would take 9 years to double your money! 20

Rule of 72 (continued) Working On Your Own: Calculate how many years will it take $1,500 to double if it grows at an interest rate of 6%? $________________________ Show your work here: 21

Rule of 72 (Now you try!) On Your Own: Calculate the number of years it will take to double your money at Interest Rates of 12%, 9%, 4%, and 2% 22 12% _____ 9%_____ 4%_____ 2%_____ What is the relationship between the rate of interest and how long it will take you to double your money? __________________________

DO NOW: Laurel and Hardy Handout (Apply Compound Interest Formula) See Handout: Laurel and Hardy start an advertising business. They hope to do well and expect to retire someday. Laurel, who turned 25, is a saver. He puts $10,000 into his retirement account right away and intends to leave it there until he turns 60 (35 years). Hardy, is more of a spender. He waits until he is 40 to put money away for his retirement. He realizes that he is way behind Laurel so he puts $20,000 into his retirement account and intends to keep it there until he is 60 (20 years). Both gentlemen shopped around and found a bank that offered 8% interest compounded daily. How much money do both of them have at age 60? 23

Exit Ticket 24 Please explain the picture below as it relates to Simple Interest vs. Compound Interest :

Exit Ticket Answer… 25

Please rate your understanding(After lesson) On a scale of 1 to 5 please rate your overall understanding of the following concepts: Savings rates Simple Interest Time value of money Compound Interest Now my overall rating is a ________. 26