What is the first payment of a $250,000 ordinary annuity whose annual payments decline by 10% each and every for the life of annuity, which is for 10 years, earning interest at 6% compounded annually? Thanks for help.
This question can be answered in a variety of ways. There is a rather involved TVM formula for these type of problems but is rarely used.
What this problem entails is to find the PV of $1 and then 90% of subsequent payments for ten years. That is: $1/1.06 + $.9/1.06^2 + .9^2/1.06^3..........etc. This can be summed up very quickly by a solver, such as Wolfram/Alpha. Here is the summation formula that I plugged in Wolfram/Alpha, which gives the answer instantaneously: ∑ [.9^n/1.06^(n+1)], n=0 to 9. It gives: 5.03312362640.
Now, we simply divide $250,000 / 5.03312362640=$49,670.94. This is the first payment of this annuity which decreases by 10% per year for 10 years.
http://www.wolframalpha.com/input/?i=%E2%88%91+%5B.9%5En%2F1.06%5E(n%2B1)%5D,+n%3D0+to+9
