Some applications involve computing interest earned on an investment during a specified time period. The interest can be computed as simple interest or compound interest.
Simple interest is based only on the initial deposit, which serves as the amount on which interest is computed, called the principal, for the entire time period. The simple interest is given by the formula
I = Prt
where I is the interest, P is the principal (starting amount), r is the rate as a decimal and t is the time in years.
The following video explains how to solve interest problems using the simple interest formula.
where V and P are in dollars.
If $10,000 is invested at a simple annual interest rate of 6 percent, what is the value of the
investment after two years?
According to the formula for simple interest, the value of the investment after 2 years is
V = ($10,000)(1 + 0.06(2)) = $11,200
In the case of compound interest, interest is added to the principal at regular time intervals, such as annually, quarterly, and monthly. Each time interest is added to the principal, the interest is said to be compounded. After each compounding, interest is earned on the new principal, which is the sum of the preceding principal and the interest just added.
If the amount P is invested at an annual interest rate of r percent, compounded annually, then the value V of the investment at the end of t years is given by the
If the amount P is invested at an annual interest rate of r percent, compounded n times per year, then the value V of the investment at the end of t years is given by the formula
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