Chapter 7: Non-annual interest rates and annuities

Question 1

p-thly effective interest rate

Answer 1

if i denotes the annual effective interest rate, the pthly interest rate for a period 1/p is
(1+i)^(1/p) -1

Question 2

pthly effective discount rate in terms of annual effective discount/interest rate

Answer 2

if d denotes the annual effective discount rate, the corresponding pthly effective discount rate (for a period of 1/p) is
=1- (1-d)^(1/p)
=1-(1+i)^(-1/p)

Question 3

Nominal rate of interest convertible pthy

Answer 3

May also be referred to as convertible
effective pthly interest by number of time periods per year. i.e i__(p)__ =p in year and effective pthly interest rate.

=p[(1+i)^(1/p) -1]

Question 4

pthly effective interest rate

Answer 4

=i__(p)__/p

Question 5

relationship between two nominal interest rates of different frequencies

Answer 5

(1+i__(p)__/p)^p=1+i=(1+i__(m)__/m)^m

Question 6

force of interest

Answer 6

limit as p approaches infinity of i__(p)__

Question 7

Nominal rate of discount convertible pthly

Answer 7

d__(p)__ = p * d__(p)__/p=p[1-(1-d)^(1/p)]=p[1-(1+i)^(-1/p)]

Amount of interest paid in a year

Question 8

relationship between nominal interest and nominal discount rates

Answer 8

(1+i__(p)__/p)^p = (1-d__(m)__/m)^-m