The interest is calculated on amount to be paid back.

     For example, you borrow $1,000 with 5% interest. So, you will only really receive $1,000 - $50 (5% of $1,000) or $950 because $50 will have to be paid back in interest.

APR = (2 x 1 x $50) / {$950 x (1+1)} = 5.263%

F = P x (1+r)^T

F = Future payment or value of the loan in future dollars

P = Principal

r = Rate of return per year

T = Time (years)

First you need to adjust...

• r = number of compounding period in 1 year

e.g. loan at 5% annual rate compounded every half a year would make

r = 5% / 2 = 2.5% per HALF year

• T = number of compounding periood

e.g. a one year loan compounded every half a year would make

T = 2

Example:

Compound interest semi-annually (2 payments 6 months apart)

F = $1,000 x (1+(5%/2))^2 = $1050.625

APR = (2 x 2 x $50.625) / {$1,000 x (2+1)} = 6.75%