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#1




Decreasing annuity problem
Francois purchases a 10year annuityimmediate with annual payments of 10X.
Jacques purchases a 10year decreasing annuityimmediate which also makes annual payments. The payment at the end of year 1 is equal to 50. At the end of year 2, and at the end of each year through year 10, each subsequent payment is reduced over what was paid in the previous year by an amount equal to X. At an annual effective interest rate of 7.072%, both annuities have the same present value. Calculate X, where X < 5. Answer: 3.59 Can someone please explain why you can't use the decreasing annuity formula ( [n aanglen] /i ) to solve this? I did 10X aangle10 = X(Da)angle10 at 7.072% And when in general can you use the decreasing annuity formula and when can you not? 
#2




The payments under the stated decreasing annuity, are 50, 50X, .........., 50 9X, while to use the standard decreasing annuity formula X would have to be 5. Use the more general P,Q formula with P = 50 and Q = 5.

#4




the Da formula without a leading coefficient is the pattern n, n1, n2,...,1. This can be scaled with a multiple. You are really better off never using the Da, and Ia formulas and just using the P,Q formula. Da angle n is P = n, Q=1. The P,Q formula can be adapted to any arithmetic sequence and any number of payments..

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