Question

Read the discussion question posted below, then post a comment of at least 200 words.

How are the simple rate, the periodic rate, and the effective annual rate related? Can you think of a situation where all three of these rates will be the same?

Answer 1

Generally Loans are issued stating an Interest rate.

Stated Interest rate would be same in all the three cases but difference comes in method of calculated Interest rate.

In Simple interest the stated rated rate is directly applied to principal to arrive at interest earned.

In Periodic interest the stated rate is applied to principal and also on Accumulated interest over number of periods.

Effective Annual Interest is actual interest or income received from an investment during the period divided by Principal amount.

Lets make an example:

Principal - 100

Stated Interest rate - 10%

i) Simple Interest - 100 X 10% = 10

ii) Periodic Interest ( Lets assume interest Compounded half yearly) - then interest rate for half year would be (10/2) 5%.

Interest for the First Half = 100*5% = 5

Interest for the Second Half = (100+5) = 5.25

Total Interest under periodic method = 10.25

iii) Effective interest is the actual amount received divided by principal. It is (10/100*100)10% for the first case and (10.25/100*100) 10.25 % for the second case.

The result can be same in the three cases for first year when compound interest is calculated yearly where interest earned in all three cases would be 10.