Find the compound interest on $10 000 for 2 years at 7.5 % per annum compounded annually.

Compound interest is defined as the interest added to the principal amount of a deposit or a loan in order for the added interest to earn interest from then on. 

The formula to calculate compound interest is as follows: 

`A = P (1 + i) ^n`

Where: 

A = Accumulated amount (Principal + interest) 

P = Principal amount (initial amount invested or initial loan amount) 

i = Interest rate per conversion period (decimal amount)

n = number of conversion periods 

Let's write down the information we have. 

P = $10000

i = 7.5/100 = 0.075

n = 2 * 1 = 2 (conversions is per annum over a two year period)  

A = ?  - What we are looking for. 

`A = 10000 (1 + 0.075)^2`

`A = $11556.25` 

The compound interest, I, is calculated as follows: 

`I = A - P = $11556.25 - $10000 = $1556.25`

The total compound interest is $1556.25