Compound interest is the combination of interest earned on the principal during the current period and  all previous interest earned but not paid for previous periods. In other words, you earn "interest on interest". With simple interest, the lender only earns interest on the principal amount per annum. For periods of less than year, the lender will receive a pro rata share of the annual interest. For compound interest, all prior interest is added to the principal amount, effectively increases the annual rate earned by the lender. The use of compound interest and the compounding frequency are established in the loan documents.
 The formula to calculate compound interest in a year is: compoundinterest=(P(1+i)n−P){\displaystyle compoundinterest=(P(1+i)^{n}-P)}. In the formula, the variables stand for the following:

P: Principal, the initial amount borrowed or deposited. 

i: Interest rate in percentage. The interest rate must be adjusted for the number of compounding periods in a year by dividing the interest rate by the number of periods. For example, a 12 percent interest rate compounded monthly would be adjusted to 1 percent (12/12).

n: Number of Compounding periods in a year multiplied by the loan period in years. Semi-annual compounding is 2, quarterly is 4, monthly is 12, and daily is 360 or 365 depending upon the financial institution.
 Solve for i in the equation. This is the interest rate adjusted for the compounding periods per year. For example, a 10 percent loan compounded monthly would have an interest rate of 10/12 or 0.00833. (1 + i) in the formula above would be (1 + .00833), or 1.00833.
 Multiply the number of periods per year by the duration of the loan. For example, a 10 year year loan would have 120 periods (10*12).
 This is represented by the figure P(1+i)n{\displaystyle P(1+i)^{n}}  in the formula. Raise the figure is parentheses to the power of n (the number of periods), then multiply by the principal. This will give you the future value of the account. 

For example, the future value of a $10,000 loan compounded monthly at 10% interest would be $27,059.
 Subtract the present value of the loan (the principal) from the future value to arrive at the interest paid over the full ten year period: $27,059 - $10,000 = $17,059.Note that the actual amount may vary depending upon the number of decimal places in the interest rate.

Calculating the compound interest rate for a single year uses the same formula adjusting for the principal amount each year. For example, the first year’s interest on a $10,000 loan compounded monthly at 10% would be $1,047. To calculate the second year’s interest, add the previous year’s interest ($1,047) to the principal amount ($10,000) and recalculate. Interest for the second year would be $1,156.

There are a number of free compound interest calculators on the Internet.
Understand compound interest.
Learn the compound interest formula.
Find the interest rate.
Solve for the number of compound periods over the term of the loan.
Solve for the future value of the loan.
Subtract the principal to get interest expense.
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