Interest is a fee that a borrower pays to a lender for a borrowed asset. This asset is typically money, but it may also be anything with a tangible value. The value of the asset is commonly referred to as the principal of the loan. The interest rate is the speed at which the interest accrues and is frequently expressed as a percentage of the asset's value. The amount of the interest is dependent upon the interest rate, the value of the borrowed asset and the length of time for which it's borrowed.
Simple Interest
Simple interest is calculated only on the principal and not on the accrued interest. This may be expressed mathematically as I = Prn where I is the simple interest and P is the principal. The interest rate for the time period over which the interest is applied is r, and the number of time periods in the term of the loan is n. Assume a loan of $2,500 has an annual interest rate of 0.1299 and that simple interest is to be applied to the loan each month. The interest rate must therefore be expressed as the monthly rate, or 0.1299/12. The interest on a 3-month loan may then be calculated as I = Prn = 0.1299/12 * $2,500 * 3 = $81.19.
Compound Interest
Compound interest is calculated on the total balance of the loan. In other words, the borrower is charged interest on the principal in addition to any previously accrued interest. The calculation of compound interest is provided by the equation I = B0 * [(1 + r)^n -- 1]. The initial balance of the loan if B0, r is the interest rate for the compounding period and n is the number of compounding periods. For example, a loan of $2,500 has an annual interest rate of 0.1299 to be compounded monthly. The interest after 3 months will be I = B0 * [(1 + r)^n -- 1] = $2,500 * [(1 + 0.1299/12)^3 -- 1] = $2,500 * (1.010825^3 -- 1) = $82.07. The balance on the loan after 3 months is therefore $2,500 + $82.07 = $2,582.07.
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