Bài giảng môn học Quản trị kinh doanh - Chapter twelve: Compound interest and present value

Chapter TwelveCompound Interest and Present ValueCopyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/IrwinCompare simple interest with compound interest.Calculate the compound amount and interest manually and by table lookup.Explain and compute the effective rate (APY).LU 12-1 Compound Interest (Future Value) – The Big PictureLearning unit objectivesLU 12-2 Present Value -- The Big PictureCompare present value (PV) with compound interest (FV).Compute present value by table lookup.Check the present value answer by compounding.Compounding 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) – The final amount of the loan or investment at the end of the last periodCompounding TermsCompounding Periods Interest CalculatedCompounding Annually Compounding Semiannually Compounding Quarterly Compounding Monthly Compounding Daily Once a yearEvery 6 monthsEvery 3 monthsEvery monthEvery dayFuture Value of $1 at 8% for Four Periods (Figure 12.1)Number 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$1.3605Future Value of $1 at 8% for Four Periods (Figure 12.1)Manual CalculationTools for Calculating Compound InterestNumber of periods (N) Number of years multiplied by 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:Semiannually: Quarterly: PeriodsRate 4 x 1 = 44 x 4 = 164 x 2 = 88% / 1 = 8%Annually:Semiannually: Quarterly: 8% / 4 = 2%8% / 2 = 4%Simple Versus Compound InterestBill Smith deposited $80 in a savings account for 4 years at an annual interest rate 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 interest rate of 8%. What is Bill’s interest and compounded amount?Interest: $108.83 -- $80.00 = $28.83SimpleCompoundedCalculating Compound Amount by Table LookupStep 1. Find the periods: Years multiplied by number of times interest is compounded in 1 year.Step 2. Find the rate: Annual rate divided by number of times interest is compounded in 1 year.Step 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 for the compound amount of $1.Step 4. Multiply the table factor by the amount of the loan. This gives the compound amount. Future Value of $1 at Compound Interest (Table 12.1)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?Periods (N) = 4 x 5 = 20Rate (R) = 6%/4 = 1.5%Table Factor = 1.3469Compounded Amount:$8,000 x 1.3469 = $10,775.20 Nominal and Effective Rates (APY) of Interest Truth in Savings LawAnnualPercentageYieldEffective rate (APY) = Interest for 1 year PrincipalNominal Rate (stated rate) – The rate on which the bank calculates interest Calculating Effective Rate APYNominal and Effective Rates (APY) of Interest Compared (Figure 12.3)Compounding Interest Daily (Table 12.2)Compounding Interest DailyUse Table 12.2 to calculate what $1,500 compounded daily for 5 years will grow to at 7%.N = 5R = 7%Factor, 1.4190$1,500 x 1.4190 = $2,128.50Present Value of $1 at 8% for Four Periods (Figure 12.4)Number of periodsPresent value goes from the future value to the present valuePresent value$.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 year.Step 2. Find the rate: Annual rate divided by number of times interest is compounded in 1 year.Step 3. Go down the Period column of the table to the number desired; look across the row to find the rate. At the intersection of the two columns is the table factor for the compound value of $1.Step 4. Multiply the table factor by the future value. This is the present value.Present Value of $1 at End Period (Table 12.3)Comparing Compound Interest (FV) (Table 12.1) with Present Value (PV) (Table 12.3)Compound value Table 12.1 Table Present Future12.1 Value Value1.3605 x $80 = $108.84(N = 4, R = 8%)We know the present dollar amount and find what the dollar amount is worth in the future.We know the future dollar amount and find what the dollar amount is worth in the present.Present value Table 12.3Table Future Present12.3 Value Value.7350 x $108.84 = $80.00 (N = 4, R = 8%)Calculating 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?Periods (N) = 4 x 4 = 16Rate (R) = 8%/4 = 2%Table Factor = .7284Compounded Amount:$20,000 x .7284 = $14,568 Invest Today