chap1 - Math 618 Notes Chapter 1 Interest rate j for a...

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Math 618 Notes Chapter 1 Interest rate j for a period: X = value at the beginning, Y = value at the end. Then Y - X X = j or Y = (1 + j ) X. Example The interest rates are i 1 for the first year, i 2 the second year, and i 3 the third year. If $100 is deposited in the beginning of the first year, what is the accumulated amount A at the end of the third year? Answer: A = 100(1 + i 1 )(1 + i 2 )(1 + i 3 ) If i 1 = i 2 = i 3 = i , then A = 100(1 + i ) 3 . Notation: We will use α ( t ) as the factor for accumulated amount after t periods. For example, for 5 years ubder a period rate of i , the factor is α (5) = (1 + i ) 5 . Effective annual rate Example If the monthly rate is 0.5%, the original amount P becomes P (1 + . 005) 12 = P (1 . 0616778) at the end of the year. This is equivalent to an annual rate of 6.16778%, the effective annual rate. Simple (annual) rate i : α ( t ) = 1 + ti , A ( t ) = A (0)(1 + ti ) where t is usually m/ 12 (in months) or d/ 365 (in days). Example
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chap1 - Math 618 Notes Chapter 1 Interest rate j for a...

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