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

This preview shows pages 1–2. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online