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Unformatted text preview: 07/08 Semester II THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT1802 Financial Mathematics Tutorial 1 1 Review 1.1 Basic Definition Interest: Compensation that a borrower of capital pays to a lender of capital for its use. Principal: Initial amount of money (capital) borrowed or invested. Period: Unit in which time is measured. 1.2 Formulas 1. The amount function A ( t ) A ( t ) = k * a ( t ) and A (0) = k 2. The interest earned during the n-th period I n = A ( n )- A ( n- 1) for n ≥ 1 3. Effective rate of interest i n = A ( n )- A ( n- 1) A ( n- 1) = I n A ( n- 1) = a ( n )- a ( n- 1) a ( n- 1) 4. Effective rate of discount d n = A ( n )- A ( n- 1) A ( n ) = I n A ( n ) = a ( n )- a ( n- 1) a ( n ) 1 5. Force of interest δ t = A ( t ) A ( t ) = a ( t ) a ( t ) e R t δ r dr = a ( t ) 1.3 Simple basis 1. Simple interest basis a ( t ) = 1 + it 2. Effective rates i n = i 1 + i ( n- 1) d n = i 1 + in 3. Determining time periods Interest earned = P * i *...
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This note was uploaded on 04/17/2011 for the course STAT 1802 taught by Professor Dr.k.c.yuen during the Spring '08 term at HKU.
- Spring '08