Kinh tế học - Chapter 12: Compound interest and present value

Chapter 12Compound Interest and Present ValueCompare simple interest with compound interestCalculate the compound amount and interest manually and by table lookupExplain and compute the effective rateCompound Interest and Present Value#12Learning Unit ObjectivesCompound Interest (Future Value) – The Big PictureLU12.1Compare present value (PV) with compound interest (FV)Compute present value by table lookupCheck the present value answer by compoundingCompound Interest and Present Value#12Learning Unit ObjectivesPresent Value -- The Big PictureLU12.2Compounding Interest (Future Value)Compound interest - the interest on the principal plus the interest of prior periodsCompounding - involves the calculation of interest periodically over the life of the loan or investmentPresent value - the value of a loan or investment todayFuture value (compound amount) - is the final amount of the loan or investment at the end of the last periodCompounding TermsCompounding Periods Interested CalculatedCompounding Annually Once a yearCompounding Semiannually Every 6 monthsCompounding Quarterly Every 3 monthsCompounding Monthly Every monthCompounding Daily Every dayFigure 12.1 Future Value of $1 at 8% for Four PeriodsNumber of periodsCompounding goes from present value to future valuePresent valueAfter 1 period $1 is worth $1.08After 2 periods $1 is worth $1.17After 3 periods $1 is worth $1.26Future ValueAfter 4 periods $1 is worth $1.36$1.00$1.08$1.1664$1.2597$1.3605Figure 12.1 Future Value of $1 at 8% for Four PeriodsManual CalculationTools for Calculating Compound InterestNumber of periods (N) Number of years multiplied the number of times the interest is compounded per yearRate for each period (R) Annual interest rate divided by the number of times the interest is compounded per yearIf you compounded $100 for 4 years at 8% annually, semiannually, or quarterly What is N and R?Annually: 4 x 1 = 4Semiannually: 4 x 2 = 8Quarterly: 4 x 4 = 16Annually: 8% / 1 = 8%Semiannually: 8% / 2 = 4%Quarterly: 8% / 4 = 2%PeriodsRateSimple Versus Compound InterestBill Smith deposited $80 in a savings account for 4 years at an annual interestrate of 8%. What is Bill’s simple interest and maturity value?I = P x R x TI = $80 x .08 x 4I = $25.60MV = $80+ $25.60MV = $105.60Bill Smith deposited $80 in a savings account for 4 years at an annual interestrate of 8%. What is Bill’s interest and compounded Amount?SimpleCompoundedInterest: $108.83 - $80.00 = $28.83SimpleCalculating Compound Amount by Table LookupStep 1. Find the periods: Years multiplied by number of times interest is compounded in 1 yearStep 2. Find the rate: Annual rate divided by number of times interest is compounded in 1 yearStep 3. Go down the period column of the table to the number desired; look across the row to find the rate. At the intersection is the table factorStep 4. Multiply the table factor by the amount of the loan. Calculating Compound Amount by Table LookupPam Donahue deposits $8,000 in her savings account that pays 6% interest compounded quarterly. What will be the balance of her account at the end of 5 years?N = 4 x 5 = 20R = 6% = 1.5% 1Table Factor = 1.3469Compounded Amount:$8,000 x 1.3469 = $10,775.20 Nominal and Effective Rates (APY) of Interest Truth in Savings LawAnnualPercentageYieldEffective Rate = Interest for 1 year (APY) PrincipalNominal Rate (Stated Rate) - The rate on which the bank calculates interest. Calculating Effective Rate APYBlue, 8% compounded quarterlyPeriods = 4 (4 x 1)Percent = 8% = 2% 4Principal = $8,000Table 12.1 lookup: 4 periods, 2% 1.0824 x $8,000Less $8,659.20 $8,000.00 659.20APY 659.20 = .0824 $8,000 = 8.24%Sun, 8% compounded semiannuallyPeriods = 2 (2 x 1)Percent = 8% = 4% 2Principal = $8,000Table 12.1 lookup: 2 periods, 4% 1.0816 x $8,000Less $8,652.80 $8,000.00 652.80APY 652.80 = .0816 $8,000 = 8.16%Figure 12.3 - Nominal and Effective Rates (APY) of Interest ComparedAnnualSemiannualQuarterlyDaily$1,060.00$1,060.90$1,061.40$1,061.806.006.09%6.14%6.18%$1,000+ 6% Beginning Nominal rate Compounding End Effective rate balance of interest period balance (APY) of interestCompounding Interest DailyCalculate by Table 12.2 what $1,500 compounded daily for 5 years will grow to at 7%N = 5R = 7%Factor 1.4190$1,500 x 1.4190 = $2,128.50Figure 12.4 Present Value of $1 at 8% for Four PeriodsNumber of periodsPresent value goes from the future value to the present valuePresent value$.7350$.7938$.8573$.9259$1.0000Future ValueCalculating Present Value by Table LookupStep 1. Find the periods: Years multiplied by number of times interest is compounded in 1 yearStep 2. Find the rate: Annual rate divided by number of times interest is compounded in 1 yearStep 3. Go down the period column of the table to the number desired; look across the row to find the rate. At the intersection is the table factor.Step 4. Multiply the table factor by the future value. This is the present value.Table 12.3 - Present Value of $1 at End PeriodComparing Compound Interest (FV) Table 12.1 with Present Value (PV) Table 12.3Compound value Table 12.1 Present value Table 12.3Table Present Future Table Future Present12.1 Value Value 12.3 Value Value1.3605 x $80 = $108.84 .7350 x $108.84 = $80.00(N = 4, R = 8) (N = 4, R = 8)We know the present dollar amount and find what the dollar amount is worth in the futureWe know the future dollar amount and find what the dollar amount is worth in the presentCalculating Present Value Amount by Table LookupRene Weaver needs $20,000 for college in 4 years. She can earn 8% compounded quarterly at her bank. How much must Rene deposit at the beginning of the year to have $20,000 in 4 years?N = 4 x 4 = 16R = 8% = 2% 4Table Factor = .7284Compounded Amount:$20,000 x .7284 = $14,568 Invest Today