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Graham is the beneficiary of an annuity due. At an annual effective interest rate of 5%, the present value of payments is 123,000. Tyler uses

Graham is the beneficiary of an annuity due. At an annual effective interest rate of 5%, the present value of payments is 123,000. Tyler uses the first-order Macaulay approximation to estimate the present value of Graham’s annuity due at an annual effective interest rate 5.4%. Tyler estimates the present value to be 121,212. Calculate the modified duration of Graham’s annuity at 5%.

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