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COMPOUNDING
FUTURE VALUE OF A PRESENT SUM
FUTURE VALUE OF A SERIES OF PAYMENTS
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Assume that you deposit $5,000$5,000 at a compound interest rate of 8% for 2 years2 years.
Future Value of a Present Sum (Graphic)
Future Value of a Present Sum (Graphic)
0 1 22
$5,000$5,000
FVFV22
8%
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COMPOUNDING
FUTURE VALUE OF A PRESENT SUMFV n = PVO (1+i)n
OR
FUTURE VALUE = PRESENT VALUE * (1 + COMPOUND RATE) CONVERSION PERIODS
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FVFV11 = PP00 (1+i)1 = $5,000$5,000 (1.08) = $5,400$5,400
Compound InterestYou 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)
Future Value of a Present Sun (Formula)
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FVFV11 = PP00 (1+i)1 = $5,000$5,000 (1.08) = $5,400$5,400
FVFV22 = FV1 (1+i)1 = {PP0 0 (1+i)}(1+i) = PP00 (1+i)2
=$5,000$5,000(1.08)(1.08)= $5,000$5,000(1.08)2
= $5,832.00$5,832.00You earned an EXTRA $32.00$32.00 in Year 2 with
compound over simple interest.
Future Value of Present Future Value of Present Sum (Formula)Sum (Formula)Future Value of Present Future Value of Present Sum (Formula)Sum (Formula)
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FVFV11 = P0(1+i)1
FVFV22 = P0(1+i)2
General Future Value Future Value Formula:
FVFVnn = P0 (1+i)n
or FVFVnn = P0 (FVD FVD i n) -- See Table See Table A1A1
General Future Value FormulaGeneral Future Value Formula
etc.
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FVD FVD I,n is found in Table A1
Valuation Using Table IAValuation Using Table IA
Period 6% 7% 8% 1 1.060 1.070 1.080 2 1.124 1.145 1.166 3 1.191 1.225 1.260 4 1.262 1.311 1.360 5 1.338 1.403 1.469
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FVFV22 = $5,000 (FVD FVD 8%,2)= $5,000 (1.166)
= $5,830 $5,830 [ due to [ due to rounding]rounding]
Using Future Value TablesUsing Future Value Tables
Period 6% 7% 8%1 1.060 1.070 1.0802 1.124 1.145 1.1663 1.191 1.225 1.2604 1.262 1.311 1.3605 1.338 1.403 1.469
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PROBLEM:$5000 @ 8% COMPOUNDED
ANNUALLY FOR 3 YEARS
FV n = 5000*(1.08)3
FV n =5000(1.259712) = 6,298.56
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PROBLEM:$5000 @ 8% COMPOUNDED
QUARTERLY FOR 3 YEARS
FV n = 5000*(1.02)12
FV n =5000(1.2682418) = 6,341.21
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Julie Miller wants to know how large her $10,000$10,000 deposit will become at a compound interest rate of 10% for 5 years5 years.
Example ProblemExample Problem
0 1 2 3 4 55
$10,000$10,000
FVFV55
10%
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Calculation based on Table A1:FVFV55 = $10,000 (FVD FVD 10%, 5)
= $10,000 (1.6105) = $16,105$16,105
Problem SolutionProblem Solution
Calculation based on general formula:FVFVnn = P0 (1+i)n
FVFV55 = $10,000 (1+ 0.10)5
= $16,105.10$16,105.10