# Annuity Question

• Jan 18th 2009, 11:20 AM
linzi_4
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!
• Jan 18th 2009, 12:04 PM
jonah
Quote:

Originally Posted by linzi_4
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
$
\begin{array}{l}
A = \sum\limits_{n = 1}^6 {1,000\left( {1.12} \right)^{ - n} } = 1,000\frac{{1 - \left( {1.12} \right)^{ - 6} }}{{0.12}} \\
\Leftrightarrow A \approx 4,111.407324... \\
\end{array}
$

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