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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 Insured Accounts Consumer Math 2012-2013 2 Overview • Differences between checking and savings accounts • APR vs. APY • CDs • MMAs • Simple Interest • Compound Interest 3 • Interest Earned Differences – 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 http://instacalc.com/4968 6 Example 1 • If your credit card company charges 1% a month APR, what % is that a year? APR = 1% x 12 APR = 12% per year 7 Example 2 • If your credit card company charges 1% a month APY, what % is that a year? APY = (1+.01%)^(12)-1 APY = 12.68% 8 Lesson 4 End • Review • Quiz 9 Simple Interest A=P+PxRxT • Simple Interest – Money you receive solely based off of a principal amount • • • • • A = Final amount I = Interest Earned Principle = original invested amount R = % Rate (as a decimal) T = Time in years 10 Example 3 • 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? Interest = 3,050 x 0.021 x 1 = 64.05 Total Amount = 3,050 + 64.05 = 3,114.05 11 Example 4 • You have a choice between 3 bank accounts. Which one should you choose to make the most simple interest? 1. Principle = $1,200, Rate = 3%, Time = 3 years 2. Principle = $1,200, Rate = 2%, Time = 4 years 3. Principle = $1,200, Rate = 5%, Time = 2 years 1. 1200 x .03 x 3 = $108 2. 1200 x .02 x 4 = $96 3. 1200 x .05 x 2 = $120 12 Compound Interest • 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 (APR as a decimal) t = number of years n = number of times the interest is compounded per year 13 Principle = $1,000 & APR = 10% • Simple Interest (Non-compounding): Year 1 Year 2 Start Year 3 Start Year 4 Start $1,000 $1,100 $1,200 $1,300 Interest on $1000 = $100 Interest on $1000 = $100 Interest on $1000 = $100 • Compound Interest (Annual Compounding): Year 1 Year 2 Start Year 3 Start Year 4 Start $1,000 $1,100 $1,210 $1,331 Interest on $1000 = $100 Interest on $1,100 = $110 Interest on $1,210 = $121 14 Simple vs. Compound • • • • Principal = $2,000 Rate = 5% Time = 6 years Compounded Annually Simple Interest A = 2000+2000 x .05 x 6 A = $2,600 Compounded Interest A = 2000(1+(.05/1))^(1*6) A = $2,680.19 15 16 Compound Interest Calculator http://www.ultimatecalculators.com/future_val ue_annuity_calculator.html • Retirement Time Horizon: • Assumed Interest Rate: • Compounded Annually 17 Example 6 1. 2. 3. 4. Simple Interest, P = $10,000, APR = 6%, T = 8 Years Compounded Annually, P = $10,000, APR = 5%, T = 8 years Compounded Daily, P = $10,000, APR = 5%, T = 8 years Accept $13,000 8 years from now. 1. A = 10000+ 10000 x .06 x 8 2. A = 10000(1+(.05/1))^(1*8) 3. A = 10000(1+(.05/365))^(365*8) 4. A = NO INTEREST! = $14,800 = $14,774.55 = $14,917.84 = $13,000 18 Example 7 • 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. A = 5000 + 5000 x 0.05 x 5 = $6,250 19 Example 8 • 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. A = 5000 x (1+(.05/1))^(1 x 5) = $6,381.41 20 Example 9 1. Bank of Anthony: Simple Interest, P = $10,000, APR = 6%, T = 10 Years 2. Bank of Daisy: Compounded Annually, P = $10,000, APR = 5.5%, T = 10 years 3. Bank of Bree: Compounded Semiannually, P = $10,000, APR = 5%, T = 10 years 4. Bank of Jennifer: Compounded Monthly, P = $10,000, APR = 4.9%, T = 10 years 5. Bank of Luis: Compounded Daily, P = $10,000, APR = 4.8%, T = 10 years 21 Example 9 1. Bank of Anthony: = $16,000 Simple Interest, P = $10,000, APR = 6%, T = 10 Years 2. Bank of Daisy: = $17,081.44 Compounded Annually, P = $10,000, APR = 5.5%, T = 10 years 3. Bank of Bree: = $16,386.16 Compounded Semiannually, P = $10,000, APR = 5%, T = 10 years 4. Bank of Jennifer: = $16,306.88 Compounded Monthly, P = $10,000, APR = 4.9%, T = 10 years 5. Bank of Luis: = $16,160.23 Compounded Daily, P = $10,000, APR = 4.8%, T = 10 years 22 Federal Deposit Insurance Corporation • FDIC • Insures low risk investments – Checking – Savings – Certificates of Deposits – Money Market Accounts • Limit up to $250,000 per bank where your money is stored – (Up from $100,000 before Financial Meltdown) 23 CDs – Certificates of Deposit • Your principal is “locked in” for a fixed period of time (6 months, 1 year, 5 years, etc.) • Typically offers higher interest rate when compared with savings accounts • Low Risk • Some are variable rate • Bankrate.com 24 CD’s Continued • Locked in period expires = Reach Maturity – You may take out or add to your principal during “Grace Period” – If you take out money before Grace Period, you are subject to penalties (60 days interest) – Penalties are just on interest collected. Never on principal • To calculate interest lost, 1. Divide APR (as a decimal) by 12. 2. Multiply that decimal answer by principal 3. Multiply that answer by the number of months charged by fee 4. You will lose that much in interest • If fee >interest, you lose all interest accumulated 25 26 27 APR or APY? • APR does not take compounding into effect • APY does take compounding into effect • When performing calculations, ALWAYS USE APR • When comparing accounts, ALWAYS USE APY 28 Example 10 • You decide to purchase a 3 year CD that has an APR of 1.3%. It compounds daily. What will be the amount in the CD once it reaches maturity? 29 Example 11 • You invest $10,000 in a 5 year CD that has an APR of 1.5%. It compounds monthly. – What will be the amount in the CD once it reaches maturity? – You need money to buy Christmas presents, and take out your money. There is a 2 month penalty. About how much interest will you lose? 30 Review of Interest • • • • Always use APR in calculations Simple Interest = P + P*R*T Compound Interest = P(1+(r/n))^(n*t) Calculate simple and daily compounded interest on $30,000 over 1 year. 31 Simple & Compound Interest Example 32 Money Market Accounts • Like a savings account where you can write checks off of • Higher interest rates than savings/checking accounts • Catches: – Minimum balance • $500 and up to $50,000+ (jumbo) – Less than 5 withdrawals a month 33 Money Market Accounts • Offered by banks and credit unions • Insured by – FDIC (Banks) – NCUA – National Credit Union Association • Invests in Treasury Bills, deposits, CDs, federal funds, short term mortgages, and asset backed securities • Provides liquidity funding for global financial system • www.bankrate.com 34 35 Lesson 5 End • Review • Quiz 36