Question

If the effective interest rate is 20% per annum, What is the nominal rate if it is:
a. Compounded daily (360 days)
b. Compounded daily (365 days)
c. Compounded weekly
d. Compounded monthly
e. Compounded quarterly
f. Compounded semi-annnually
g. Compounded annually

Answer 1

Effective interest rate = 20% per annum

a) If it is compounded daily (360 days)

Daily rate of interest = 20% / 360 = 0.000556

Annual effective rate of interest [1 + 0.000556]^³⁶⁰ = 1.2213 which is 22.13% per annum

b) If it is compounded daily (365 days)

Daily rate of interest = 20% / 365 = 0.000548

Annual effective rate of interest [1 + 0.000548]^³⁶⁵ = 1.2213 which is 22.13% per annum

c) If it is compounded weekly (52 weeks)

Daily rate of interest = 20% / 52 = 0.003846

Annual effective rate of interest [1 + 0.003846]^⁵² = 1.2209 which is 22.09% per annum

d) If it is compounded monthly (12 months)

Daily rate of interest = 20% / 12 = 0.01667

Annual effective rate of interest [1 + 0.01667]^¹² = 1.2194 which is 21.94% per annum

e) If it is compounded quartrely (4 quarter)

Daily rate of interest = 20% / 4 = 0.05

Annual effective rate of interest [1 + 0.05]^⁴ = 1.2155 which is 21.55% per annum

f) If it is compounded semi annually (2 semi annual)

Daily rate of interest = 20% / 2= 0.1

Annual effective rate of interest [1 + 0.1]^² = 1.21 which is 21% per annum

g) If it is compounded annually

Daily rate of interest = 20% / 1 = 0.2

Annual effective rate of interest [1 + 0.2]^¹ = 1.2 which is 20% per annum