Question

Determine the difference between the following interest rates, if they were all used as yearly rates. In your dropbox submission calculate each rate out, and rank them from highest to lowest. In the answer box below, enter the absolute value difference between rate 1 and 4 (entered as %, so 0.2% would mean just enter "0.2" below).

Rate 1: 5.73% nominal yearly, compounded daily

Rate 2: 5.73% nominal yearly, compounded monthly

Rate 3: 5.73% nominal yearly, compounded yearly

Rate 4: (5.73% + 0.2%*) yearly

*(note for example if your problem reads 5% + 0.2% yearly this means 5.2% yearly)

Answer 1

Rate 1:

5.73% compounded daily (Assuming there are 365 days in a year) which means rate of interest of daily is 5.73% / 365 = 0.0157% per day

Annual interest rate would be = {[(1 + Daily rate of interest)^^{(365 * Number of years)}] - 1} * 100

Annual interest rate = {[(1 + 0.000157)^³⁶⁵] - 1} *100 = (1.0589 - 1) * 100 = 5.89% yearly

Rate 2:

5.73% compounded monthly (there are 12 months in a year) which means rate of interest of month is 5.73% / 12 = 0.4775% per day

Annual interest rate would be = {[(1 + Monthly rate of interest)^^{(12 * Number of years)}] - 1} * 100

Annual interest rate = {[(1 + 0.004775)^³⁶⁵] - 1} *100 = (1.0588 - 1) * 100 = 5.88% yearly

Rate 3:

5.73% compounded yearly

Annual interest rate would be = {[(1 + Yearly rate of interest)^^{(Number of years)}] - 1} * 100

Annual interest rate = {[(1 + 0.00573)^¹] - 1} * 100 = 5.73% yearly

Rate 4:

5.73% + 0.2% yearly which is 5.93% yearly

Ranking of best to worst:

Rate 4 > Rate 1 > Rate 2 > Rate 3