Compound Interest By: Sharra Jones

Introductory Activity Desmond needs $3500 to buy a car. He already has $1000 saved. He still needs $2500. Desmond is trying to decide which of the following options is best in helping him obtain the rest of the money quicker. Option A Option B He can cut 4 yards every Saturday until he has earned the money. It takes about 2 hours to mow a typical yard. Each yard brings in $25, but for every $100 he makes, Desmond must pay expenses and fees of $25. He can work for his dad at the shop every Saturday until he has earned the money. His dad will pay him $12.50 an hour and Desmond would work 8 hours each Saturday. Also, his dad agreed that for every $100 Desmond saves his dad would add an extra $25 to Desmond’s savings. © Council for Economic Education slide 2

Interest Interest is the amount of money that you pay to borrow money or the amount of money that you earn on a deposit. To calculate simple interest we use the formula I = P×r ×t I is the interest earned P is the principal or the original amount of money with which you start r is the annual interest rate as a decimal t is the time in years. © Council for Economic Education slide 3

Simple Interest Example Dianna deposits $725 into a savings account that pays 2.3% simple annual interest. How much interest will Dianna earn after 18 months? © Council for Economic Education slide 4

Solution Simple interest is interest paid only on the original principal. In the simple interest formula, time is measured in years. Write 18 months as 1.5 years. Write the annual interest rate as a decimal. I = P×r×t © Council for Economic Education slide 5

Student Exercise Problem 1 Problem 2 Principal: $550 Principal: $870 Determine the amount of interest earned. Use the formula for simple interest. Problem 1 Problem 2 Principal: $550 Principal: $870 Annual rate: 7% Annual rate: 3.7% Time: 4 years Time: 30 months © Council for Economic Education slide 6

Compound Interest Compound interest is interest that is earned on both the principal and any interest that has been earned previously. http://www.stlouisfed.org/education_resources/no- frills-money-skills/episode-1-growing-money/ © Council for Economic Education slide 7

Compound Interest   © Council for Economic Education slide 8

Example Problem Simon deposits $400 in an account that pays 3% interest compounded annually. What is the balance of Simon’s account at the end of 2 years? Step 1: Find the balance at the end of the first year. Step 2: Find the balance at the end of the second year. © Council for Economic Education slide 9

Student Exercise Principal: $600, Annual rate: 4%, Time: 3 years Balance at the end of the first year is ________. Balance at the end of the second year is ________. Balance at the end of the third year is ________. © Council for Economic Education slide 10

Example Jackie deposits $325 in an account that pays 4.1% interest compounded annually. How much money will Jackie have in her account after 3 years? © Council for Economic Education slide 11

Student Exercise Problem 1 Problem 2 Principal: $285 Principal: $1200 Annual rate: 1.9% Annual rate: 8.7% Time: 6 years Time: 2 years © Council for Economic Education slide 12

Calculator Use the compound interest calculator to work out the pervious problem. http://www.econedlink.org/interactives/index.php?iid= 2&type=educator © Council for Economic Education slide 13

Example Let's invest $100 in an account that pays 12% interest each year...and let's say that the account is compounded yearly. Compounded yearly means that, at the end of each year, they add the yearly interest (12%) to your account. (That's 12% of the amount in your account.) Jan end of Dec $100 12% $100 + .12 (100) = $112 © Council for Economic Education slide 14

Example continued What if we make the same investment, but it's compounded semi-annually? Compounded semi-annually (twice a year) means that, at the end of June, they add 6% of the amount in your account...and at the end of December, they add another 6%. Jan end of June end of Dec $100 6% 6% $100 + .06 (100) $106 + .06(1.06) = $112.36 © Council for Economic Education slide 15

Example continued Now, let's make it quarterly... Compounded quarterly (four times a year) means that, at the end of each quarter (three months), they'll add 3% to your account. (Remember that this is 3% of what's in the account at that time.) Jan end of March end of June end of Sept end of Dec $100 3% 3% 3% 3% $100 $103 $106.09 $109.27 + .03 (100) + .03 (103) +.03 (106.09) +.03 (109.27) = $103 = $106.09 = $109.27 = $112.55 © Council for Economic Education slide 16

Another Way to Calculate If we invest $100 in an account that pays 12% compounded quarterly, how much will we have in the account at the end of one year? Initial amount = $100 At the end of each period (quarter), we'll be earning 3%... So, each $100 will turn into $103 Growth factor = $103 Number of periods = 4 © Council for Economic Education slide 17

Another Example Continued Final amount = $100 × (1.03)⁴ = $112.55 Final amount = $100 × (1.03)⁴ = $112.55 © Council for Economic Education slide 18

Example If we invest $20,000 in an account that pays 8% compounded semi- annually, how much will be in the account in 15 years? Initial amount = $20,000 At the end of each period (six months), we'll be earning 4%... So, each $1.00 will turn into $1.04... Growth factor = 1.04 Number of periods = 30 (That's twice a year for 15 years.) Final amount = $20,000 × (1.04)³º = $ 64,867.95 © Council for Economic Education slide 19

Student Exercise 1) Invest $1,000 at 3% compounded yearly (just once a year) for 10 years. 2 ) Invest $1,000 at a lower rate, 2.98%, compounded monthly for 10 years. Which one is the better choice? © Council for Economic Education slide 20