Question

Your bank is offering you an account that will pay 15% interest (an effective two-year rate) in total for a two-year deposit. Determine the equivalent discount rate for the following periods: a. Six months b. One year c. One month (Note: Be careful not to round any intermediate steps less than six decimal places.) a. Six months The equivalent discount rate for a period length of six months is %. (Round to two decimal places.)

Answer 1

Ans:

Effective interest rate in total for 2 years = 15% or   0.15

Effective rate = ((1+ periodical rate)^no of periods in year) - 1     

     

(a) No of 6 months periods in 2 year = 2*2=   4

0.15 = ((1+r)^4)-1     

1.15= ((1+r)^4)     

(1.15)^(1/4) = (1+r)     

1.03555807634= (1+r)

r =   1.03555807634-1

r or 6 months rate = 0.03555807634or 3.55%

     

So equivalent rate for 6 months is 3.55%    

(b) No of one year periods in 2 year = 1*2=   2

0.15 = ((1+r)^2)-1     

1.15= ((1+r)^2)     

(1.15)^(1/2) = (1+r)     

1.07238052948= (1+r)

r =   1.07238052948   -1

r or one Year rate =   0.07238052948or 7.24%

     

So equivalent rate for one year period is 7.24%     

(c) No of one month in 2 year = 12*2=   24

0.15 = ((1+r)^24)-1     

1.15= ((1+r)^24)     

(1.15)^(1/24) = (1+r)     

1.0058404033= (1+r)

r =   1.0058404033   -1

r or 1 month rate =   0.0058404033or 0.58%

     

So equivalent rate for one month period is 0.58%