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?

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?

Answer 1

To calculate the amount you would need to spend yearly to fund the grand soirée, we can use the concept of perpetuity. A perpetuity is a stream of cash flows that continues indefinitely. The formula to calculate the annual payment needed for a perpetuity is:

Payment = Principal / Interest rate

Assuming you want to spend X amount per year for the grand soirée, you need to solve for the Principal:

Principal = Payment * Interest rate

Since the interest rate is provided as 6%, we can substitute that to find the Principal:

Principal = X / 0.06

To calculate the amount of money you need to leave to your heirs after 50 years, we can use the compound interest formula:

Future Value = Present Value * (1 + Interest rate) ^ Time

Here, the Future Value is the amount you want to leave to your heirs, the Present Value is the Principal you calculated for the grand soirée, the Interest rate is 6% (0.06), and the Time is 50 years. Substituting the values, the equation becomes:

Future Value = Principal * (1 + 0.06) ^ 50

To calculate the amount you would need to invest yearly to fully fund the annuity in 50 years, you can use the formula for the present value of an annuity:

Present Value = Payment * ((1 - (1 + Interest rate)^(-Time)) / Interest rate)

Here, you want to find the Payment, which is the amount you need to invest yearly. The Present Value is the Principal you calculated for the grand soirée, the Interest rate is 6% (0.06), and the Time is 50 years. Rearranging the formula, we can solve for the Payment:

Payment = Principal * (Interest rate / ((1 - (1 + Interest rate)^(-Time))))

Substituting the values, the equation becomes:

Payment = Principal * (0.06 / ((1 - (1 + 0.06)^(-50))))

You can now calculate the answers using the formulas provided and the values you have.