Question

1.) If the account earns an interest rate of 24% compounded monthly, find the effective rate of interest:
A. Compounded daily 360 days
B. Compounded daily 365 days
C. Compounded weekly
D. Compounded monthly
E. Compounded quarterly
F. Compounded semi-annually
G. Compounded annually

2.) What is the effective annual interest rate for a nominal interest rate of 24% compounded continuously?

Answer 1

1)

Effective interest rate = 24% per annum

a) If it is compounded daily (360 days)

Daily rate of interest = 24% / 360 = 0.000667

Annual effective rate of interest [1 + 0.000667]^³⁶⁰ = 1.2711 which is 27.11% per annum

b) If it is compounded daily (365 days)

Daily rate of interest = 24% / 365 = 0.000548

Annual effective rate of interest [1 + 0.000548]^³⁶⁵ = 1.2711 which is 27.11% per annum

c) If it is compounded weekly (52 weeks)

Daily rate of interest = 24% / 52 = 0.004706

Annual effective rate of interest [1 + 0.004706]^⁵² = 1.2765 which is 27.65% per annum

d) If it is compounded monthly (12 months)

Daily rate of interest = 24% / 12 = 0.02

Annual effective rate of interest [1 + 0.02]^¹² = 1.2682 which is 26.81% per annum

e) If it is compounded quartrely (4 quarter)

Daily rate of interest = 24% / 4 = 0.06

Annual effective rate of interest [1 + 0.06]^⁴ = 1.2625 which is 26.25% per annum

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

Daily rate of interest = 24% / 2= 0.12

Annual effective rate of interest [1 + 0.12]^² = 1.2544 which is 25.44% per annum

g) If it is compounded annually

Daily rate of interest = 24% / 1 = 0.24

Annual effective rate of interest [1 + 0.24]^¹ = 1.24 which is 24% per annum

2) Interest rate of 24% compounded continuously

Annual effective rate of interest = e^^{(r * t)}

wher value of e = 2.71828

r = 0.24

t = 1

Annual effective rate of interest = 2.71828^^*0.24 = 1.2713 which is 27.13%