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Decreasing annuities

October 26th, 2007

I think there is some confusion about the decreasing annuities notation. The coefficient is the amount each payment decreases by. It is also the last payment. The first payment is the coefficient times the number of payments.


represents the present value of payments of 15, 10, and 5. Notice the first payment is 5 x 3 and the last payment is 5.

So if we have payments of 100, 90, 80 and 70. There are 4 payments and each payment decreases by 10. So we start with:


However, that only gives us 10×4, 10×3, 10×2, 10×1 => 40, 30, 20, 10.

So we need to add a level payment of 60 to each payment. So the present value is:


I hope that clears up some of the confusion.

James Student Questions

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