COMPOUNDING FUTURE VALUE OF A PRESENT SUM FUTURE VALUE OF A SERIES OF PAYMENTS

$5,000 2 years Assume that you deposit $5,000 at a compound interest rate of 8% for 2 years. Future Value of a Present Sum (Graphic) $5,000 FV 2 8%

COMPOUNDING FUTURE VALUE OF A PRESENT SUM FV n = PV O (1+i) n OR FUTURE VALUE = PRESENT VALUE * (1 + COMPOUND RATE) CONVERSION PERIODS

FV 1 P 0 $5,000 $5,400 FV 1 = P 0 (1+i) 1 = $5,000 (1.08) = $5,400 Compound Interest You earned $400 interest on your $5,000 deposit over the first year. This is the same interest you would earn under simple interest. Future Value of a Present Sun (Formula)

FV 1 P 0 $5,000 $5,400 FV 1 = P 0 (1+i) 1 = $5,000 (1.08) = $5,400 FV 2 P 0 P 0 FV 2 = FV 1 (1+i) 1 = {P 0 (1+i)}(1+i) = P 0 (1+i) 2 $5,000 =$5,000(1.08)(1.08) $5,000 $5, = $5,000(1.08) 2 = $5, $32.00 You earned an EXTRA $32.00 in Year 2 with compound over simple interest. Future Value of Present Sum (Formula)

FV 1 FV 1 = P 0 (1+i) 1 FV 2 FV 2 = P 0 (1+i) 2 Future Value General Future Value Formula: FV n FV n = P 0 (1+i) n FV n FVD See Table A1 or FV n = P 0 (FVD i n ) -- See Table A1 General Future Value Formula etc.

FVD FVD I,n is found in Table A1 Valuation Using Table IA

FV 2 FVD $5,830 [ due to rounding] FV 2 = $5,000 (FVD 8%,2 ) = $5,000 (1.166) = $5,830 [ due to rounding] Using Future Value Tables

PROBLEM: 8% COMPOUNDED ANNUALLY FOR 3 YEARS FV n = 5000*(1.08) 3 FV n =5000( ) = 6,298.56

PROBLEM: 8% COMPOUNDED QUARTERLY FOR 3 YEARS FV n = 5000*(1.02) 12 FV n =5000( ) = 6,341.21

$10,000 5 years Julie Miller wants to know how large her $10,000 deposit will become at a compound interest rate of 10% for 5 years. Example Problem $10,000 FV 5 10%

FV 5 FVD $16,105 Calculation based on Table A1: FV 5 = $10,000 (FVD 10%, 5 ) = $10,000 (1.6105) = $16,105 Problem Solution FV n FV 5 $16, u Calculation based on general formula: FV n = P 0 (1+i) n FV 5 = $10,000 ( ) 5 = $16,105.10