120 points) As a future graduate of the University of Miami\'s prestigious Schoo
ID: 2781752 • Letter: 1
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120 points) As a future graduate of the University of Miami's prestigious School of Business ministration, someday you would like to endow a scholarship (meaning give the university money in your name) to pay for tultion expenses for future SBA students. Assume you just graduated (congratulations!). You plan to work for fifteen years after graduation before endowing this scholarship fat the end of the fifteenth year AFTER graduation). Annual tuition at UM is $10,000 today, and is expected to grow at the long term average rate of inflation of 3% per year forever. Savings isexpected to earn a return of 7% per year forever. if the first tuition payment is due one year after the scholarship is endowed, and you would like the scholarship to pay all tuition for one student per year for the twenty years following the creation of the endowment, how much money do you need to endow the scholarshlp? If you would like the scholarship to pay for tuition for one student per year forever, how much money do you need to endow the scholarship? You plan to start saving for the endowment starting your first year after graduation (meaning first savings is one year after graduation). You plan to increase the amount you save each year by 5%, because you expect to have more income per year as time goes on. How much money do you need to save in the first year, so that you will have enough to endow the scholarship from part b (that pays tuition forever)? a) b) c)Explanation / Answer
Particulars Amount ($) Annual Tution fees 10000 Inflation rate 3% Savings rate 7% Suppose the year of graduation is 2017. So 15 years after 2017 would be 2032 So scholarship would be endowed in 2032 a) First tution payment is due one year after the scholarship is endowed. So first tution payment is due in 2033. Future Value = A*[((1+i)^n)-1)/i] 1+i = (1+i)^n = ((1+i)^n)-1 = (((1+i)^n)-1)/i = A*[((1+i)^n)-1)/i] = Money needed to endow the scholarship is $ 2,68,703.74 b) The future value (FV) measures the nominal future sum of money that a given sum of money is “worth” at a specified time in the future assuming a certain interest rate, or more generally, rate of return. Perpetuities are a special type of annuity; a perpetuity is an annuity that has no end, or a stream of cash payments that continues forever. There is no end date, so there is no future value formula. To find the FV of a perpetuity would require setting a number of periods which would mean that the perpetuity up to that point can be treated as an ordinary annuity. So let us assume that perpetuity is 100 years 1+i = (1+i)^n = ((1+i)^n)-1 = (((1+i)^n)-1)/i = Future Value A*[((1+i)^n)-1)/i] = Money needed to endow the scholarship is $60,72,877.33
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