Question

(a) Calculate the effective annual rate (EAR) for each, given the nominal rate of 12%

(APR) and the following compounding frequencies: (I) quarterly (II) monthly (III) daily.

(b) Calculate the nominal rate (APR) for each, given the effective annual rate of 12% (EAR) and the following compounding frequencies: (I) quarterly (II) monthly (III) daily.

(c) Calculate the periodic rate in percent for each, given the nominal rate of 12% (APR) and the following compounding frequencies: (I) quarterly (II) monthly (III) daily.

(d) State which of the following statements are true?

(I) Nominal rate = Effective rate = Periodic rate for annual compounding.

(II) Effective rate > Nominal Rate > Periodic rate for compounding other than annual compounding.

Answer 1

Formula

a) Effective annual rate (EAR) = (1+(nominal rate/number of compounding period))^(number of compounding period)-1

b) Nominal interest rate (APR) = number of compounding period *[(1+EAR)^1/number of compounding period -1]

c) Periodic interest rate = APR/number of compounding period

Q.no	Quarter	Monthly	Daily
a)EAR	(1+(12%/4))^4-1 = 12.55%	1+(12%/12))^12-1 = 12.68%	1+(12%/365))^365-1 = 12.75%
b)APR	4*[(1+12%)^1/4-1] = 11.49%	12*[(1+12%)^1/12-1] = 11.38%	365*[(1+12%)^1/365-1] = 11.33%
c) period rate	12%/4 =3%	12%/12 =1%	12%/365 = 0.03288%

d). Effective rate > Nominal Rate > Periodic rate for compounding other than annual compounding.

Effective rate is greater than nominal and periodic interest rate.