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Statistics Help

**Question: **You wish to leave an endowment for your heirs that goes into effect 50 years from today. You don’t want to be forgotten after you pass so you wish to leave an endowment that will pay for a grand soirée yearly and forever. What amount would you like spent yearly to fund this grand party? How much money do you have to leave to your heirs 50 years from now assuming that will compound at 6% interest? Assuming that you have not invested anything today, how much would you have to invest yearly to fully fund the annuity in 50 years, again assuming a 6% monthly compounding rate? Edit

**Answer: **. Assuming that I want my heirs to get $6,000 yearly for a grand soiree yearly and forever 50 years from today and I have not invested any money now, so I need to spend $6,000 yearly at an annually compounding interest rate of 6%. The amount which my heirs will get after 50 years from now will be calculated as follows:

Future Value = Present Value * {(1+ rate of interest) No. of years– 1}/ rate of interest

Future Value = 6000 * {(1+0.06)50 -1}/0.06

Future Value = $17,42,015.43

So, I will leave for my heirs an amount of $17,42,015.43 after 50 years if I spend $6,000 today for funding the grand party.

Assuming that I have not invested anything till now, so the amount need to be invested for funding the annuity in 50 years at 6% monthly compounding rate will be calculated as follows:

Present Value = Future Value / (1+rate of interest/compounded times a year) no. of years*compound time

Present Value = 1742015.43 /(1+.06/12)50*12

Present Value = 1742015.43/19.9359

Present Value = $87,380.82

Edit

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