All I can do is remind them of the truth of Albert Einstein’s alleged response when he was asked, “What do you, Mr. Einstein, consider to be man’s greatest invention?” He didn’t reply the wheel or the lever. He is reported to have said, “Compound interest.” 1

Savings Accounts Consumer Math

Overview Differences between checking and savings accounts APR vs. APY Simple Interest Compound Interest Online vs. Physical Smart Phone 3

Differences Interest Earned – Savings: All earn interest – Checking: Few earn interest (if you meet requirements) Number of Transactions – Savings: Unlimited deposits, 3-6 withdrawals a month – Checking: Unlimited deposits/withdrawals Funds Access – Savings: Limited (in person or online transfers from one account to another) – Checking: Convenient (ATMS, in person, or online) Fees – Savings: None (if monthly withdrawals don’t go over limit) – Checking: Overdraft fees, minimum balance fees, ATM fees, Online Access fees, Bill Pay fees Bill Paying – Savings: Not usually offered with online services – Checking: Automatic withdrawals to pay loans, credit cards, gym memberships or other ongoing expenses. Single withdrawals too. 4

Interest Money you receive from a bank or institution for storing your money (principal) with them – APR (Annual Percentage Rate) – APY (Annual Percentage Yield) 5

APR vs APY APR – APR is the annual rate of interest without taking into account the compounding of interest within that year. – APY – APY does take into account the effects of intra-year compounding. Online APR -> APY Calculator 6

Example 1 If your credit card company charges 1% a month APR, what % is that a year? 7

Example 2 If your credit card company charges 1% a month APY, what % is that a year? 8

Simple Interest A = P + P x R x T Simple Interest – Money you receive solely based off of a principal amount A = Final amount I = Interest Earned Principal = original invested amount R = % Rate (as a decimal) T = Time in years 9

Your bank with pay you 2.1% APR simple interest per year. You deposit $3,050 in your savings account in January. – How much interest will you have earned in 1 year? – What is the total amount in your savings account? 10 Example 3

You have a choice between 3 bank accounts. Which one should you choose to make the most interest? – Principal = $1,200, Rate = 3%, Time = 3 years – Principal = $1,200, Rate = 2%, Time = 4 years – Principal = $1,200, Rate = 5%, Time = 2 years 11 Example 4

Compound Interest – Money you receive based off of a principal amount and any interest already added on to the principal Formula for annual compound interest A = final amount P = original invested amount (principal) r = annual % rate (as a decimal) t = number of years n = number of times the interest is compounded per year 12

Principal = $1,000 & APR = 10% Simple Interest (Non-compounding): Compound Interest (Annual Compounding): 13 $1,100 Year 2 Start $1,000 Year 1 $1,300 Year 4 Start $1,200 Year 3 Start Interest on $1000 = $100 Interest on $1000 = $100 Interest on $1000 = $100 $1,100 Year 2 Start $1,000 Year 1 $1,331 Year 4 Start $1,210 Year 3 Start Interest on $1000 = $100 Interest on $1,100 = $110 Interest on $1,210 = $121

Simple vs. Compound Principal = $2,000 Rate = 5% Time = 6 years Compounded Annually Simple Interest Compounded Interest 14

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Compound Interest Calculator ue_annuity_calculator.html Retirement Time Horizon: Assumed Interest Rate: Compounded Annually 16

Example 5 Calculate the final amount in an account receiving simple interest on an account of $5,000 at a rate of 5% APR after 5 years. 17

Example 6 Calculate the final amount in an account receiving compound interest on an account of $5,000 at a rate of 5% APR compounded annually after 5 years. 18