Question

Find the effective interest rate per payment period for an interest rate of 9% compounded monthly for each of the given payment schedule:
a. Monthly

b. Quarterly

c. Semiannual

d. Annual

Answer 1

Answer:

a. 0.75% per month

b. 2.25% per quarter

c. 4.5% semi- annually

d. 9% yearly

Explanation:

a. Computing the effective interest rate per payment period for the payment schedule which is monthly:

Effective rate (monthly) = Nominal rate (r) / Compounded monthly (m)

where

r is 9%

m is 12

Putting the values above:

= 9% / 12

= 0.75% per month

b. Computing the effective interest rate per payment period for the payment schedule which is quarterly:

Effective rate (quarterly) = Nominal rate (r) / Compounded quarterly (m)

where

r is 9%

m is 4

Putting the values above:

= 9% / 4

= 2.25% per quarter

c. Computing the effective interest rate per payment period for the payment schedule which is semi- annually:

Effective rate (semi- annually) = Nominal rate (r) / Compounded quarterly (m)

where

r is 9%

m is 2 (every 6 months)

Putting the values above:

= 9% / 2

= 4.5% semi- annually

d. Computing the effective interest rate per payment period for the payment schedule which is annually:

Effective rate (annually) = Nominal rate (r) / Compounded yearly (m)

where

r is 9%

m is 1 (end of the year)

Putting the values above:

= 9% / 1

= 9% yearly