Uncle's Will Annuity Calculation

Uncle's Will Annuity Calculation

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Question

Your distant uncle's will specifies that you will receive a 20-year annuity of $10,000 a year, the payments starting seven years from now. How much is the annuity worth to you today if your discount rate is 4% per year?

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Explanation

The payments start at the end of 7 years. Thus, at the end of year 6, the annuity will be worth 10,000/0.04*(1-1/(1.04^20)) = 135,903. The present value of this amount is 135,903/(1.04^6) = 107,406.