Compounding Interest

The two most common methods of calculating interest use the simple interest and the compound interest formulas.

Simple interest. Simple interest is the dollar cost of borrowing money. This cost is based on three elements: the amount borrowed, which is called the principal; the rate of interest; and the time for which the principal is borrowed. The formula used to find simple interest is:

interest = principal x rate of interest x amount of time the loan is outstanding

or

I = P x R x T

Example Suppose you borrow $1,000 at 10 percent simple annual interest and repay it in one lump sum at the end of 3 years. To find the amount that must be repaid, calculate the interest: Interest = $1,000 x .10 x 3 = $300 This computes to $100 of interest each year. The amount that must be repaid is the $1,000 principal plus the $300 interest or a total of $1,300.

Compound interest. Unlike simple interest, compound interest calculates interest not only on the principal, but also on the prior period's interest. The formula for calculating compound interest is:

Future repayment value = principal x (1 + rate of interest)^{amount of time}

or

F = P x (1 + R)^T

The factor (1+ R)^T can be obtained easily using pencil and paper, a calculator, or a compound interest table. Most consumer loans use monthly or, possibly, daily compounding. Thus, if you are dealing with monthly compounding, the "R" term in the above formula relates to the monthly interest rate, and "T" equals the number of months in the loan term. Likewise, if the loan in question uses daily compounding, the "R" term relates to the daily interest rate, and "T" equals the number of days in the loan term.

Example Suppose you borrow $1,000 at 10 percent interest, compounded monthly, and repay it in one lump sum at the end of three years. To find the amount that must be repaid, you must first convert the 10 percent annual interest rate into a monthly interest rate: 0.10 (or 10%) / 12 = .00833 Plugging this number into the formula yields: F = $1,000 x (1 + .00833)36 F = $1,000 x (1.00833)36 F = $1,000 x (1.34802) F = $1,348.02

Financial Calculators How interest is calculated can greatly affect your savings. The more often interest is compounded, or added to your account, the more you earn. The Compound Interest Calculator will demonstrate how compounding can affect your savings, and how interest on your interest really adds up!

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