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Class 6 and 7 Before

# O then o and the ear r yr that corresponds to a

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O Then O And the EAR r Yr that corresponds to a continuously compounded interest rate i cont is given by:

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7 Example: Continuous Compounding O What is the effective annual rate of return for a nominal rate of 12% compounded continuously?
8 Here We Go Again ( ) ( ) ( ) ( ) ( ) Yr i Yr daily i Yr mo i Yr Q i Yr semi i r e r r r r r r r r cont daily mo Q semi + = + = + = + + = + = + + = + = + + = + = + 1 1 1 1 1 ) 1 ( 1 1 ) 1 ( 1 1 ) 1 ( 1 365 365 365 12 12 12 4 4 4 2 2 2

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9 A Picture Says More O This picture shows the effective annual interest rates (y-axis) for a nominal interest rate of 12% as a function of the number of compounding periods per year (x-axis). EAR 12.00% 12.75% 1 365 Compounding periods per year 2 12.36% 4 12.55%
10 Continuous Compounding for more than one Year O A firm borrows \$1,300 at a continuously compounded interest rate i = 8%. The firm repays the loan after 3 years. How much does the firm have to pay at the end of 3 years? O We are looking for FV 3 . After one year: After two years: After three years: O So in our case:

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11 Alternatively O A firm borrows \$1,300 at a continuously compounded interest rate i = 8%. The firm repays the loan after 3 years. How much does the firm have to pay at the end of 3 years? O We are looking for FV 3 .
Annuities 12

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13 Annuities O An annuity is a series of level cash flows that occur at the end of each period for a finite number of periods. – Important: O The present value of an annuity is the amount of money you would need today to duplicate the cash flows associated with the annuity (for a given interest rate).
14 Annuities and the Timeline O An annuity is a series of level payments/cash flows that occur at the end of each period for a finite number of periods.

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