COMPOUNDING

FUTURE VALUE OF A PRESENT SUM

FUTURE VALUE OF A SERIES OF PAYMENTS

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%

COMPOUNDING

FUTURE VALUE OF A PRESENT SUMFV n = PVO (1+i)n

OR

FUTURE VALUE = PRESENT VALUE * (1 + COMPOUND RATE) CONVERSION PERIODS

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)

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)

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.

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

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

PROBLEM:$5000 @ 8% COMPOUNDED

ANNUALLY FOR 3 YEARS

FV n = 5000*(1.08)3

FV n =5000(1.259712) = 6,298.56

PROBLEM:$5000 @ 8% COMPOUNDED

QUARTERLY FOR 3 YEARS

FV n = 5000*(1.02)12

FV n =5000(1.2682418) = 6,341.21

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%

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