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Math Help - Annuity Question

  1. #1
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    Annuity Question

    Q10 - You want to buy an annuity that will pay you 1000 per year for the next 6 years. The first payment will be made to you in one year's time. What is the maximum you should pay, if you estimate that you could achieve a return of 12% pa on the money?

    We have been given the answer - it is 3604.78, but we have to show how to get this answer.
    I have tried lots of different formulas but cant get this answer, the closest I've been is 2692 by using this formula =6000*((1-(12.5/100))^6). I'm not sure which is the correct formula as I have tried working out present value and future value, but neither seem to work!

    If anyone could just point me in the right direction that would be a great help.

    Thanks!
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  2. #2
    Member jonah's Avatar
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    Quote Originally Posted by linzi_4 View Post
    Q10 - You want to buy an annuity that will pay you 1000 per year for the next 6 years. The first payment will be made to you in one year's time. What is the maximum you should pay, if you estimate that you could achieve a return of 12% pa on the money?

    We have been given the answer - it is 3604.78, but we have to show how to get this answer.
    I have tried lots of different formulas but cant get this answer, the closest I've been is 2692 by using this formula =6000*((1-(12.5/100))^6). I'm not sure which is the correct formula as I have tried working out present value and future value, but neither seem to work!

    If anyone could just point me in the right direction that would be a great help.

    Thanks!
    If an annuity will pay you 1000 per year for the next 6 years, then
    <br />
\begin{array}{l}<br />
 A = \sum\limits_{n = 1}^6 {1,000\left( {1.12} \right)^{ - n} }  = 1,000\frac{{1 - \left( {1.12} \right)^{ - 6} }}{{0.12}} \\ <br />
  \Leftrightarrow A \approx 4,111.407324... \\ <br />
 \end{array}<br />

    If an annuity will pay you 1000 per year for the next 5 years, then
    <br />
\begin{array}{l}<br />
 A = \sum\limits_{n = 1}^5 {1,000\left( {1.12} \right)^{ - n} }  = 1,000\frac{{1 - \left( {1.12} \right)^{ - 5} }}{{0.12}} \\ <br />
  \Leftrightarrow A \approx 3,604.776202... \\ <br />
 \end{array}<br />
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