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We can also express Modified duration as follows:
...Eq. (3)
The expression in the brackets of the modified duration formula is given by equation (3) and is a measure created by Frederick Macaulay in 1938. This measure is known as Macaulay duration. Actually Macaulay duration is nothing but the weighted-average term to maturity of the cash flows from a bond. The weight of each cash flow is determined by dividing the present value of the cash flow by the price. Rewriting the formula of modified duration, we get:
a. Consider the time line below that shows periodic cash flows and interest rates per period. Interest rate/year 0 1 2 3 4 5 6 7 8 9 Time 2,500 -4,000 6,000 -3,700 Cash flows
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