At the age of 75, Mrs. Walker decided to set up a trust fund for her grandson, which can take care of some of his expenses for the rest of his life. She made an initial contribution of $150 000 to set up the trust fund, which would make the first semi-annual payment of perpetuity to her grandson, 5 years from now. If the funds in trust earn 5% compounded annually, what is the maximum payment the trust can make to Mrs. Walker's grandson in perpetuity?

Question

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The maximum payment the trust can make to Mrs. Walker's grandson in perpetuity is $4613.74. This is because the trust fund will earn 5% compounded annually, which means that the value of the fund will double every 14 years. The first payment will be made 5 years from now, so the value of the fund will have doubled by then. The second payment will be made 10 years from now, so the value of the fund will have doubled again. This process will continue indefinitely, so the value of the fund will continue to grow at a rate of 5% per year. The maximum payment that the trust can make is the amount of interest that the fund earns each year. This amount is equal to 5% of the value of the fund, which is $150,000. Therefore, the maximum payment that the trust can make is $4613.74.

At the Age of 75, Mrs