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Econ. Lecture 3 Economic Equivalence and Interest Formula’s Read Problems 2.6, 2.8, 2.11, 2.14, 2.15

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First an example from last lecture Single Payment To Find Given Functional Notation Compound Amount Factor F P(F/P, i, n) Present Worth Factor P F(P/F, i, n) This notation refers to interest tables in the back of your text, Appendix C. The table works out multiplication factors for a given interest rate over a given number of years.

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Example: To raise money for a business, a person asks for a loan from you. They offer to pay you $3000 at the end of four years. How much should you give him if you want 12%/year on your money? P = unknown n = 4 years i = 12% F = $3000 P = F/(1+i) n = 3000/ (1+0.12) 4 = $

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With the Interest Tables P = F(P/F,i,n) = 3000(P/F,12%,4) = 3000 (0.6355) = $ Slight difference in the answer that you get is minimal.

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Back to Equivalence Economic equivalence – exists between cash flows that have to same economic effect Economic indifference – if two cash flows are equal to each other, we don’t care which is chosen

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There are four simple principles of Equivalence: 1) Alternatives require a common time basis – A point in time will be used that best fits the analysis of our alternatives, given P,F 2) Dependent on interest rate 3) May require conversion of multiple payments to a single payment 4) Equivalence is maintained regardless frame of reference

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Example of Principle One: Deposit $4000 today and 10%. In 15 years you have $16, How much do you have after 10 years?

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From both time directions find V 10 ? F = $4000(F/P,10%,10)= $4000 (2.5937) = $ P = $16,708.80(P/F, 10%,5) = $16, (0.6209) = 10, Equal in time!

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Five types of cash flows 1) Single Cash Flow – one P or F 2) Uniform Series – equal payment series, equal series of payments for n years 3) Linear Gradient – changing payment by a constant amount G, in each cash flow

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4) Geometric Gradient – changing payment by a constant percentage, g, in each cash flow 5) Irregular Series – no overall regular pattern in payment scheme

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Uneven Cash Flow When presented with an uneven payment series, the F or P can be calculated by summing the individual payments.

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Example: For the given cash flow, determine F at 30 years, 4%. F? Example: For the given cash flow, determine F at 30 years, 4%.

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F = 3000(F/P,4%,23) + 800(F/P,4%,20) (F/P,4%,17) + 400(F/P,4%,5) = 3000*(2.4647) + 800*(2.1911) *(1.9479) + 400*(1.1699) = = $17,016.96

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Uniform Payment Series

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Consider the following situation:

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F = A + A(1+i) + A(1+i) 2 (1) In this case, n = 3, equation (1) can be written as: F = A + A(1+i) + A(1+i) n-1 (2)

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Multiplied by (1+i): (1+i)F = A(1+i) +A(1+i) n-1 +A(1+i) n (3) Subtract (2) F = A + A(1+i) + A(1+i) n-1 Equals iF = -A + A(1+i) n

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Equal Payment Series compound amount Factor or Uniform Series Compound Amount (F/A,i,n)

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