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2. Your child is about to enter college a year from now. A local foundation provides...

2. Your child is about to enter college a year from now. A local foundation provides scholarships (essentially interest-free loans) each year perpetually for students. Your child has won the scholarship just now. When your child joins college, he/she would receive a scholarship of $ 10,000 per year annually for 4 years. Your child is expected to repay the scholarship amount of $ 40,000 in 15 equal yearly installments, interest-free beginning a year after the expiration of his/her scholarship. The foundation seems to be giving an interest free loan. The market interest rate is 8% and would not change in the future. a. What is the PV of the scholarship? b. If the foundation invests a lump sum today to fund all future scholarships. What must be that investment today?

a. What is the PV of the scholarship?

b. If the foundation invests a lump sum today to fund all future scholarships. What must be that investment today?

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Answer #1

a)PV of Scholorship

given risk free rate is 8% taken as discount rate to findout PV

scholorship givens at begining of the year .so PV facor @ 8% for year -0 ,year-1, year -2 ,Year-3 are 1, 0.926, 0.857 , 0.793.

Particulars Amount
year-0 10000 x 1 10000
Year-1 10000 x 0.926 9260
Year -2 10000 x 0.857 8570
Year -3 10000 x 0.793 7930
Total 35760

b)Investement today

as per info we take market interest rate is dicount rate, to fund the scholorship per student would be pv of scholorship i,e 35,760 only

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