Jeff deposits 10 into a fund today and 20 fifteen years later. interest is credited at a nominal discount rate of d compounded quarterly for the first 10 years, and at a nominal interest rate of 6% compounded semiannually thereafter. the accumulated balance in the fund at the end of 30 years is 100. calculate d

The following series of payments has present value zero: Contributions 10 20 100 Time (in years) 0 15 30 The present value at time 10 of the payments at time 15 and at time 30 is â’20(1.03) to the power -10 + 100(1.03) to the power -40 = â’14.8818 + 30.6557 = 15.7738 This equals the present value at time 10 of the initial deposit, i.e. 10(1â’d/4) to the power -40 = 15.7738 So, d = 4.5318%

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