Question

The nominal annual interest rate compounded quarterly is 24.36%. It is desired to find in which of the following ranges does the equivalent nominal annual discount rate compounded eight times per year lie? Possible Answers A < 23.25% B 223.25% but <23.50% c23.50% but <23.75% D 23.75% but <24.00% 24.00%

Answer 1

E.>= 24.00%

first let us know the effective annual rate =( 1 +r/n)^n -1

here,

r = 24.36%

n= 4 (since we have quarterly compounding).

effective annual rate = (1 +0.2436/4)^4-1

=> (1.26677008)-1

=>0.26677008.

=>26.68%.

now,

equivalent nominal discount rate compounded 8 times per year whose effective annual rate is 26.68% is to be found out.

effective annual rate = (1+r/n)^n-1

here,

r is to be found out

n = 8 times

=>0.2668 = (1+ r/8)^8 -1

=>1.2668 = (1+ r/8)^8

=> 1.2668 ^(1/8) = 1+r/8

=>1.03000304=1 + r/8

=>0.03000304 = r/8

=>r=0.24002432

=>24.00%.