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 15% simple annual rate into annual rate, compounded semi-annually.

Show all work. Label and clearly explain your answer.

Answer 1

As per rules I am answering the first 4 subparts of the question

a: Simple annual rate= Simple monthly rate*12 = 3%*12 = 36%

b: Annual rate compounded monthly = (1+r/m)^m-1

where r is the nominal rate and m is the frequency of compounding

= (1+6%/12)^12-1

=6.17%

c:

First find the effective rate of 9% compounded monthly as (1+9%/12)^12-1=0.093807

Find the rate which when compounded daily gives the same effective rate

Daily compounded rate=r

(1+r)^(365)-1 = Effective rate

(1+r)^(365)= 1.093807

r= 0.000245685

Daily compounded rate= 0.000245685*365= 8.97%

d: Annual rate= (1+r/m)^m-1

= (1+12%/52)^52-1

= 1.002308^52-1

= 12.73%