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21 June, 02:54

Your father is about to retire, and he wants to buy an annuity that will provide him with $78,000 of income a year for 25 years, with the first payment coming immediately. The going rate on such annuities is 5.15%. How much would it cost him to buy the annuity today

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  1. 21 June, 06:43
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    The annuity would cost him $1,082,988.93

    Explanation:

    To find the answer, we use the present value of an annuity formula:

    P = A [ (1 - (1 + i) ^-n) / i ]

    Where:

    P = Present value of the annuity (the value we are looking for) A = Value of the annuity payments ($78,000 in this case) i = interest rate (in this case 5.15% or 0.0515) n = number of compounding periods (in this case: 25 years)

    Now, we plug the amounts into the formula and solve:

    P = $78,000 [ (1 - (1 + 0.0515) ^-25) / 0.0515]

    P = $1,082,988.93
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