Fin320-CH5 - FIN 320 Chapter #5: The Time Value of Money...

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  FIN 320 Chapter #5: The Time Value of Money Christo Pirinsky
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  Learning Objectives Explain the mechanics of compounding, which is how money grows over a time when it is invested. Be able to move money through time using time value of money tables, financial calculators, and spreadsheets. Discuss the relationship between compounding and bringing money back to present.
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  Learning Objectives Define an ordinary annuity and calculate its compound or future value. Differentiate between an ordinary annuity and an annuity due and determine the future and present value of an annuity due. Determine the future or present value of a sum when there are nonannual compounding periods.
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  Learning Objectives Determine the present value of an uneven stream of payments Determine the present value of a perpetuity. Explain how the international setting complicates the time value of money.
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  Principles Used in this Chapter Principle 2 : The Time Value of Money – A Dollar Received Today Is Worth More Than a Dollar Received in The Future.
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  Simple Interest Interest is earned on principal $100 invested at 6% per year 1 st year interest is $6.00 2 nd year interest is $6.00 3 rd year interest is $6.00 Total interest earned: $18.00
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  Compound Interest When interest paid on an investment during the first period is added to the principal; then, during the second period, interest is earned on the new sum.
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  Compound Interest Interest earned on previously earned interest $100 invested at 6% with annual compounding 1 st year interest is $6.00 Principal is $106.00 2 nd year interest is $6.36 Principal is $112.36 3 rd year interest is $6.74 Principal is $119.11 Total interest earned: $19.11
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  Future Value - The amount a sum will grow in a certain number of years when compounded at a specific rate.
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  Future Value  FV FV n n = PV (1 + i) = PV (1 + i) n Where Where FV FV n n = = the future of the investment at the future of the investment at the end of year the end of year n n . . i= i= the annual interest (or discount) the annual interest (or discount) rate rate PV = PV = the present value, or original the present value, or original amount invested at the beginning amount invested at the beginning of the of the first year first year
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  Future Value Example 1 Suppose you invest $1000 for one year at 5% per year. What is the future value in one year? Interest = 1000(.05) = 50 Value in one year = principal + interest = 1000 + 50 = 1050 Future Value (FV) = 1000(1 + .05) = 1050 Suppose you leave the money in for another year. How much will you have two years from now? FV = 1000(1.05)(1.05) = 1000(1.05) 2 = 1102.50
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  Effects of Compounding Simple interest Compound interest Consider the previous example FV with simple interest = 1000 + 50 + 50 = 1100 FV with compound interest = 1102.50 The extra 2.50 comes from the interest of .05(50) = 2.50 earned on the first interest payment
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  Effects of Compounding
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Fin320-CH5 - FIN 320 Chapter #5: The Time Value of Money...

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