Simple interest = Principal x interest rate x time

 

For example:

     Someone lends you $1,000 to buy a computer at 5% interest. You must repay the total amount at the end of 1 year.

Principal = $1,000

Interest rate = 5%

Time = 1 year

Therefore,

Simple interest = $1,000 x 5% x 1 = $50

And,

APR = (2 x 1 x $50)/ {$1000 x (1 + 1)} = 5%

Example:

Using the above example of $1,000 loan and 5% interest. Instead of making one payment at the year end, you are now making 2 payments every 6 months.

The first payment:

Simple interest = $1,000 x 5% x 1/2 = $25

(note that: time is now half a year, denoted by 1/2 in the equation)

So, your first payment = $500 (principal) + $25 (interest) = $525

 

The second payment:

Simple interest = $500x 5% x 1/2 = $12.50

(note that: time is again half a year, denoted by 1/2 in the equation and the principal is now $500)

So, your second payment = $500 (principal) + $12.50 (interest) = $512.50

 

Total pay:

Altogether, you pay $525 + $512.50 = $1037.50

This makes APR = (2 x 2 x ($25+$12.50))/{$1,000 x (2+1)} = 0.05 or 5%

 

So, for simple interest, it makes no difference how often you repay.