Topic 9: Integration, interest rates, present value and difference equations

Question 1

What is the periodic rate (1)

Answer 1

-The annual rate of interest divided by the number of interest periods per year

Question 2

What is the continuous growth formula (2)

Answer 2

-S_t = S₀e^rt
-This shows how much a principal S₀ will have increased after t years if the annual interest rate is r and if there is continuous compounding of interest

Question 3

What is the continuous proportional growth rate of S_t (1)

Answer 3

-S’_t/S_t

Question 4

What is the discount factor appropriate for t years (1)

Answer 4

-(1+r)^-t

Question 5

What are the formulas for discrete + continuous compound interest (2)

Answer 5

Suppose amount k is due for payment in t years, present value A with interest rate = r

-Discrete compound interest: A = K(1+r)^-t
-Continuous compound interest: A = ke^-rt

Question 6

What is a first-order difference equation (1)

Answer 6

-One that relates the value of a function in period t+1 in only the previous period t