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COMPOUNDING

COMPOUNDING. FUTURE VALUE OF A PRESENT SUM FUTURE VALUE OF A SERIES OF PAYMENTS. Future Value of a Present Sum (Graphic). Assume that you deposit $5,000 at a compound interest rate of 8% for 2 years. 0 1 2. 8%. $5,000. FV 2. COMPOUNDING.

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COMPOUNDING

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  1. COMPOUNDING • FUTURE VALUE OF A PRESENT SUM • FUTURE VALUE OF A SERIES OF PAYMENTS

  2. Future Value of a Present Sum (Graphic) Assume that you deposit $5,000 at a compound interest rate of 8% for 2 years. 0 12 8% $5,000 FV2

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

  4. Future Value of a Present Sun (Formula) FV1 = P0 (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.

  5. Future Value of Present Sum (Formula) FV1 = P0(1+i)1 = $5,000 (1.08) = $5,400 FV2 = FV1 (1+i)1 = {P0 (1+i)}(1+i) = P0(1+i)2 =$5,000(1.08)(1.08) = $5,000(1.08)2 = $5,832.00 You earned an EXTRA$32.00 in Year 2 with compound over simple interest.

  6. General Future Value Formula FV1 = P0(1+i)1 FV2 = P0(1+i)2 General Future Value Formula: FVn = P0 (1+i)n or FVn = P0 (FVD in) -- See Table A1 etc.

  7. Valuation Using Table IA FVD I,nis found in Table A1

  8. Using Future Value Tables FV2 = $5,000 (FVD 8%,2) = $5,000 (1.166) = $5,830 [ due to rounding]

  9. PROBLEM: $5000 @ 8% COMPOUNDED ANNUALLY FOR 3 YEARS FV n = 5000*(1.08)3 FV n =5000(1.259712) = 6,298.56

  10. PROBLEM: $5000 @ 8% COMPOUNDED QUARTERLY FOR 3 YEARS FV n = 5000*(1.02)12 FV n =5000(1.2682418) = 6,341.21

  11. Example Problem Julie Miller wants to know how large her $10,000 deposit will become at a compound interest rate of 10% for 5 years. 0 1 2 3 4 5 10% $10,000 FV5

  12. Problem Solution • Calculation based on general formula:FVn = P0 (1+i)nFV5= $10,000 (1+ 0.10)5 = $16,105.10 • Calculation based on Table A1: FV5= $10,000(FVD 10%, 5)= $10,000(1.6105) = $16,105

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