Question

a. Convert 3% simple monthly rate into simple annual rate. b. Convert 6% simple annual rate into annual rate, compounded monthly. c. Convert 9% annual rate compounded monthly into annual rate, compounded daily. d. Convert 12% annual rate, compounded weekly into simple annual rate. e. Convert 24% simple annual rate to annual rate, compounded continuously. Show All Work.

Answer 1

a)

Simple Annual Rate = Simple Monthly Rate*12 = 3*12 = 36%

Effective Interest Rate or EAR = [{1+(APR/n)}^n]-1

Where, APR = Annual Interest Rate or Nominal Rate, n = Number of times compounded in a year

Accordingly,

b)

For Monthly,

EAR = [{1+(0.06/12)}^12]-1 = 0.0616778 = 6.1678%

c)

For Monthly,

0.09 = [(1+i)^12]-1

1.09 = (1+i)^12

i = (1.09^1/12)-1 = 0.007207

APR = Above i*12 = 0.007207*12 = 0.0864879

For Daily,

EAR = [{1+(0.0864879/365)}^365]-1 = 0.090327= 9.0327%

d)

For Weekly,

0.12 = [(1+i)^52]-1

1.12 = (1+i)^52

i = (1.12^1/52)-1 = 0.00218

Simple Annual Rate = Above i*52 = 0.00218*52 = 0.1134477 = 11.3448%

e)

Continuosly Compounded Annual Rate = [e^APR]-1 = [e^0.24]-1 = 1.2712(from table)-1 = 0.2712 = 27.12%