A $5,000,000 estate is to be settled among 3 surviving children aged 10, 15, 20 years old. The will stipulates that the 3 children receive annual annuity payments proportional to their ages!. In other words, the oldest child will receive 100% more money than the youngest child and the middle child 50% more. The arrangement is for 10 years only. After that, each child will receive annual payments of equal amount, indexed for inflation at 2.5% per year for the rest of their natural lives. For this purpose, this inheritance is to be amortized over a period of 100 years. The trustee of the estate guarantees them a rate of 7% compounded annually. What are the payments of the 3 children for the first 10 years and their payments after that? Thanks for any help.
Boy! This is a relatively complicated calculation, since it involves using several TVM fomulas. For the sake of brevity(and since I can't really type), I will give the answers only for now, since all the relevant formula are already programmed into my computer. If the poster of the question or any of the Moderators or anybody else for that matter, has any problems or questions, then you are welcome to ask here. That being out of the way, here we go:
1- $77,867.52- Annual payment that the youngest child receives for the first 10 years.
2- $116,801.28 -Annual payment that the middle child receives for the first 10 years.
3- $155,735.04 -Annual payment that the oldest child receives for the first 10 years.
After the first 10 years, the provisions of the estate change. Taking these new conditions into account, including the inflation rate of 2.5% P.A., we have the following:
After the first 10 years, the balance of the estate will be:$4,994,420.37, which is very close to the original amount of $5,000,000. Why? Because the interest of 7% covers virtually ALL their payments, which collectively come to:$350,403.84. The principal is only being encroached by about $404 per annum. Based on this, their annual payments, with 2.5% inflation rate included, will be:
$76,517.22 that each child will receive annually for the rest of their natural lives. This amount will increase each year by 2.5%, being the inflation rate stipulated in the will. In about 28 years this amount will double at 2.5% inflation rate provided for in the will. Any questions??!!.
