Question

Given a nominal annual interest rate of 7.5% convertible every five days, determine the sum of the equivalent:
(i) force of interest; and
(ii) nominal annual discount rate compounded quarterly.
Note: There are 365 days in a year. Give your answer as a decimal rounded to four places.

Answer 1

(i)

Compute the force of interest using the equation as shown below:

Force of interest = log ( 1 + Nomina annual interest rate)

= log( 1 + 7.5%)

= 7.232066158%

Hence, the force of interest is 7.2320661258%.

(ii)

Compute the annual effective discount rate using the equation as shown below:

Annual effective discount rate = 1 - Exp(-Force of interest)

= 1 - Exp( - 7.232066158%)

= 6.976744186%

Hence, the annual effective discount rate is 6.976744186%.

Compute the number of compounding period using the equation as shown below:

Number of compounding period = Total days / Number of days after compounding

= 365 / 5

= 73

Hence, the number of compounding periods is 73.

Compute the nominal discount rate using the equation as shown below:

1 - effective discount = [ 1 - (Nominal discount / Number of compounding period)]^(Number of compounding period

1 - 6.976744186% = [1 - ( Nominal discount / 73)]^(73)

93.02325581 = [1 - ( Nominal discount / 73)]^(73)

Soliving the above equation:

Nominal discount = 7.227%.