wealthy graduate of a local university wants to establish a scholarship to cover the full cost of one student each year in perpetuity at her university. To adequately prepare for the administration of the scholarship, the university will begin awarding it starting in three years. The estimated full cost of one student this year is $32,000 and is expected to stay constant in real terms in the future. If the scholarship is invested to earn an annual real return of 10 percent, how much must the donor contribute today to fully fund the scholarship?

wealthy graduate of a local university wants to establish a scholarship to cover the full cost of one student each year in perpetuity at her university. To adequately prepare for the administration of the scholarship, the university will begin awarding it starting in three years. The estimated full cost of one student this year is $32,000 and is expected to stay constant in real terms in the future. If the scholarship is invested to earn an annual real return of 10 percent, how much must the donor contribute today to fully fund the scholarship?

Financial Accounting Intro Concepts Meth/Uses

14th Edition

ISBN:9781285595047

Author:Weil

Publisher:Weil

ChapterA: Appendix - Time Value Of Cash Flows: Compound Interest Concepts And Applications

Section: Chapter Questions

Problem 23E

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Comprehensive The following are three independent situations: 1. K. Herrmann has decided to set up a scholarship fund for students. She is willing to deposit 5,000 in a trust fund at the end of each year for 10 years. She wants the trust fund to then pay annual scholarships at the end of each year for 30 years. 2. Charles Jordy is planning to save for his retirement. He has decided that he can save 3,000 at the end of each year for the next 10 years, 5,000 at the end of each year for Years 11 through 20, and 10,000 at the end of each year for Years 21 through 30. 3. Patricia Karpas has 200,000 in savings on the day she retires. She intends to spend 2,000 per month traveling around the world for the next 2 years, during which time her savings will earn 18%, compounded monthly. For the next 5 years, she intends to spend 6,000 every 6 months, during which time her savings will earn 12%, compounded semiannually. For the rest of her life expectancy of 15 years, she wants an annuity to cover her living costs. During this period, her savings will earn 10% compounded annually. Assume that all payments occur at the end of each period. Required: 1. In Situation 1, how much will the annual scholarships be if the fund can earn 6%? How much at 10%? 2. In Situation 2, (a) How much will Charles have at the end of 30 years if his savings can earn 10%? How much at 6%? (b) If Charles expects to live for 20 years in retirement, how much can he withdraw from his savings at the end of each year if his savings earn 10%? How much at 6%? (c) How much would Charles need to invest today to have the same amount available at the time he retires as calculated in Situation 2(a) at 10%? How much at 6%? 3. In Situation 3, how much will Patricias annuity be?
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