This preview shows pages 1–9. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Chapter 1. The Growth of Money UPDATED ACTSC231 Mathematics of Finance Department of Statistics and Actuarial Science University of Waterloo Fall 2010 Instructor: Chengguo Weng C. Weng (c2weng@uwaterloo.ca) p. 1/4 7 Interest (p10) Money has time value XBox investment opportunities theory. XBox time preference theory. (p10) Interest is the payment by a borrower to a lender (investor) in return for the use of the capital. XBox Interest may be paid annually, monthly, weekly, or daily...... = continuously. XBox The original sum invested (or borrowed) is the capital or principal . XBox The total repaid is the principal plus interest. C. Weng (c2weng@uwaterloo.ca) p. 2/4 7 Example 1.1. John lends Tom $10,000 for 5 years. Tom offers the following three options of repayments: Opt1 : Pay $10,500 at the end of 5 years. Opt2 : Pay $100 at the end of each year, and repay the principal after 5 years. Opt3 : Make payment of principal and interest of $2,100 at the end of each year. Which option is most favorable for John and which one is best for Tom? John: Get money back earliest in option 3. So, option 3 is most desired. Tom: Pay money at a latest time in option 1. So, option 1 is the best choice. C. Weng (c2weng@uwaterloo.ca) p. 3/4 7 Accumulation Function (p11) Consider a single investment of $1 at time 0 without any withdrawal up to time t > XBox At time t , the accumulated value (or accumulation ) of the investment is the total of the principal plus interest added. XBox Notation: a ( t ) is used to denote the accumulation at time t of $1 invested at time 0. RHD a ( t ) as a function of t is called accumulation function. RHD a (0) = 1 RHD if interest is positive, a ( t ) is an increasing function of t C. Weng (c2weng@uwaterloo.ca) p. 4/4 7 Amount Function (p11) We use A K ( t ) to denote the accumulated value at time t of $ K invested at time 0. XBox Is it true: A K ( t ) = K a ( t ) ? RHD It may not be true e.g. A bank account earns 3% if K 5000 , and 2.5% otherwise. XBox Unless stated otherwise, we generally assume A K ( t ) = K a ( t ) . C. Weng (c2weng@uwaterloo.ca) p. 5/4 7 Example 1 of accumulation functions (p1213) e.g.1. a ( t ) = 1 + 0 . 05 t (simple interest). 5% of original capital is added each year, paid continuously. Graph of a ( t ) : C. Weng (c2weng@uwaterloo.ca) p. 6/4 7 Example 2 of accumulation functions (p1213) e.g.2. a ( t ) = 1 + 0 . 05 t , XBox where t denotes the floor of t , i.e. the integer part of t . XBox interest is added only at the end of year Graph of a ( t ) : C. Weng (c2weng@uwaterloo.ca) p. 7/4 7 Example 3 of accumulation functions (p1213) e.g.3. a ( t ) = 1 . 05 t (compound interest)....
View Full
Document
 Fall '09
 Chisholm

Click to edit the document details