Question

Your grandparents would like to establish a trust fund that will pay you and your heirs $225,000 per year forever with the first payment one year from today. If the trust fund earns an annual return of 4.4 percent, how much must your grandparents deposit today?

Answer 1

To establish a trust fund that pays $225,000 annually with a 4.4% return rate, the grandparents need to deposit $5,113,636.36 today.

Step-by-step explanation:

The student's question is related to finding the present value of a perpetuity. A perpetuity is a type of payment that continues indefinitely, and its present value can be calculated using a financial formula that accounts for the periodic payments and the interest rate. The formula for the present value of a perpetuity is PV = C / r, where PV is the present value, C is the annual payment, and r is the annual interest rate (expressed in decimal form).

To solve the problem for the student, we use the information provided: the yearly payment (C) is $225,000, and the annual return rate (r) is 4.4% (or 0.044 in decimal form).

The calculation for the present value of this perpetuity would be:

PV = $225,000 / 0.044

PV = $5,113,636.36

Therefore, the student's grandparents would need to deposit $5,113,636.36 today to establish a trust fund that can pay $225,000 per year forever, assuming a return rate of 4.4%.

Answer 2

They must deposit $5,113,636.36.

Step-by-step explanation:

Giving the following information:

Cash flow= $225,000

Interest rate= 4.4 percent

To determine the amount to be deposited today, we need to use the perpetual annuity formula:

PV= Cf/i

Cf= cash flow

PV= 225,000/0.044

PV= $5,113,636.36

They must deposit $5,113,636.36.