This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: 1 Computing Interest Rates: Some Formulas and Concepts 1.1 Simple vs. Compounded Interest Rates These notes go over some formulas and concepts useful for computing interest rates, present values, future values, etc. . . when the frequency of payments varies or when interest rates are quoted in simple or compounded terms. Let’s begin with the simplest case: a pure discount bond. Remember that this is a bond that has an initial price P (0) and a final price at some date T , P ( T ) . It pays nothing in between. Note: T need not be equal to 1. The interest rate is the implicit ratio of final price to initial price (which is also equal to the definition of rate of return we used in the second set of slides): P (0)(1 + r ) = P ( T ) Definition - Compounded interest rate: We compound an interest rate when we assume the interest (income) gained earns interest as well (a simple interest rate is when we do not assume that “interest earns interest”). For example, suppose we see a bank deposit quoting a quarterly rate of 6% for a year deposit. If this rate is quoted as a simple interest rate, $1 invested will be converted to: (1 + 4 * . 06) = 1 . 24 But if the rate is quoted as compounded, $1 dollar invested will yield, (1 + 0 . 06) 4 = 1 . 2624 It should be clear that for the same quoted rate, simple interest yields less than compounded interest. Let’s move to another important concept: rates with different periodicity of payments. Suppose a bank offers two deposits:with different periodicity of payments....
View Full Document