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1-2 Chapter 12 Compound Interest and Present Value McGraw-Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved.

1-3 Compare simple interest with compound interest Calculate the compound amount and interest manually and by table lookup Explain and compute the effective rate Compound Interest and Present Value #12 Learning Unit Objectives Compound Interest (Future Value) - The Big Picture LU12.1

1-4 Compare present value (PV) with compound interest (FV) Compute present value by table lookup Check the present value answer by compounding Compound Interest and Present Value #12 Learning Unit Objectives Present Value -- The Big Picture LU12.2

1-5 Compounding Interest (Future Value) Compound interest - the interest on the principal plus the interest of prior periods Compounding - involves the calculation of interest periodically over the life of the loan or investment Present value - the value of a loan or investment today Future value (compound amount) - is the final amount of the loan or investment at the end of the last period

1-6 Figure 12.1 Future Value of $1 at 8% for Four Periods Number of periods Compounding goes from present value to future value Present value After 1 period $1 is worth $1.08 After 2 periods $1 is worth $1.17 After 3 periods $1 is worth $1.26 Future Value After 4 periods $1 is worth $1.36 $1.00 $1.08 $ $1.2597$1.3605

1-7 Compounding Terms Compounding PeriodsInterested Calculated Compounding AnnuallyOnce a year Compounding SemiannuallyEvery 6 months Compounding QuarterlyEvery 3 months Compounding MonthlyEvery month Compounding DailyEvery day

1-8 Simple Versus Compound Interest Al Jones deposited $1,000 in a savings account for 5 years at an annual simple interest rate of 10%. What is Al’s simple interest and maturity value? I = P x R x T I = $1,000 x.10 x 5 I = $500 MV = $1,000 + $500 MV = $1,500 I = P x R x T I = $1,000 x.10 x 5 I = $500 MV = $1,000 + $500 MV = $1,500 Al Jones deposited $1,000 in a savings account for 5 years at an annual compounded rate of 10%. What is Al’s interest and compounded amount? SimpleCompoundedCompounded Compound amount $1, $1,000 = $610.51

1-9 Tools for Calculating Compound Interest Number of periods (N) Number of years times the number of times the interest is compounded per year Rate for each period (R) Annual interest rate divided by the number of times the interest is compounded per year If you compounded $100 for 3 years at 6% annually, semiannually, or quarterly What is N and R? Annually:3 x 1 = 3 Semiannually: 3 x 2 = 6 Quarterly:3 x 4 = 12 Annually:6% / 1 = 6% Semiannually: 6% / 2 = 3% Quarterly:6% / 4 = 1.5% Periods Rate

1-10 Calculating Compound Amount by Table Lookup Step 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 Step 4. Multiply the table factor by the amount of the loan.

1-11 Table Future Value of $1 at Compound Interest

1-12 Calculating Compound Amount by Table Lookup Steve Smith deposited $1,000 in a savings account for 4 years at an semiannual compounded rate of 8%. What is Steve’s interest and compounded amount? N = 4 x 2 = 8 R = 8% = 4% 2 Table Factor = Compounded Amount: $1,000 x = $1, I = $1, $1,000 = $368.60

1-13 Nominal and Effective Rates (APY) of Interest Truth in Savings Law Annual Percentage Yield Effective Rate = Interest for 1 year (APY) Principal Nominal Rate (Stated Rate) - The rate on which the bank calculates interest.

1-14 Figure Nominal and Effective Rates (APY) of Interest Compared Annual Semiannual Quarterly Daily $1, $1, $1, $1, % 6.14% 6.18% $1,000+ 6% Beginning Nominal rate Compounding End Effective rate balance of interest period balance (APY) of interest

1-15 Table Compounding Interest Daily

1-16 Compounding Interest Daily Calculate what $2,000 compounded daily for 7 years will grow to at 6% N = 7 R = 6% Factor $2,000 x = $3,043.80

1-17 Figure 12.4 Present Value of $1 at 8% for Four Periods Number of periods Present value goes from the future value to the present value Present value $.7350 $.7938 $.8573 $.9259 $ Future Value

1-18 Calculating Present Value by Table Lookup Step 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. Step 4. Multiply the table factor by the future value. This is the present value.

1-19 Table Present Value of $1 at End Period

1-20 Calculating Present Value Amount by Table Lookup Steve Smith needs $1, in 4 years. His bank offers 8% interest compounded semiannually. How much money must Steve put in the bank today (present) to reach his goal in 4 years? N = 4 x 2 = 8 R = 8% = 4% 2 Table Factor =.7307 Compounded Amount: $1, x.7307 = $1, Invest Today

1-21 Comparing Compound Interest (FV) Table 12.1 with Present Value (PV) Table 12.3 Compound value Table 12.1 Present value Table 12.3 Table Present FutureTable Future Present 12.1 Value Value12.3 Value Value x $1,000 = $1, x $1, = $1,000 (N = 8, R = 4) 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