Worked Example: The Future Value of an Annuity



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Your financial adviser tells you that you'll need to have $2 million to fund your retirement. You plan to work for another 30 years before retiring. You will make 30 contributions to a pension plan. The first contribution will be made one year from now and the last will be made 30 years from now, on the day you retire. How much will each contribution have to be to ensure that you have $2 million in your pension plan account on your retirement day if the pension plan guarantees a return of 9% p.a.?

This problem can be represented in the form of a time line as follows:

|Year |0 |1 |… |30 |

|Cash Flows | |a |… |a |

|Future Value | | | |2mm |

Using the formula for the future value of an annuity yields:

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in which case a=14,672.68.

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