Problem 1 A university plans to set up a scholarship fund for students. To establish the...

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Problem 1 A university plans to set up a scholarship fund for students. To establish the fund deposits of $20,000 are to be made at the end of each year starting in the current year. The fund is to be used to pay out an annual scholarship of $10,000 in perpetuity. The scholarship will not commence until there are sufficient funds accumulated to pay the annual amount in perpetuity. Assume that the fund will earn an interest rate of i = 0.08 per annum. a. Determine the minimum number of deposits required to be made to accumulate to enough total funds to provide the annual scholarship amount in perpetuity. b. It has been decided that the required number of full $20! 000 payments will be made to establish the fund before commencing to pay the first scholarship. It is proposed that a second scholarship should be paid with an annual scholarship of $7,000, in perpetuity, but starting a number of years after the first scholarship commences. Find the earliest time that the second scholarship can commence if no additional funds are to be deposited and the accumulated funds are used to fund both scholarships. Problem 2 Consider a set of cash flows with present value given by (Ia)Toli + v10 (Dai a. Set out a cash flow diagram showing the amount and timing of cash flows corresponding to this present value and explain your answer. b. Prove that the following relationship holds: (Ia)10+ v0 (Da) = oli oli and explain clearly why this relationship holds using your cash flow diagram in a). Problem 1 A university plans to set up a scholarship fund for students. To establish the fund deposits of $20,000 are to be made at the end of each year starting in the current year. The fund is to be used to pay out an annual scholarship of $10,000 in perpetuity. The scholarship will not commence until there are sufficient funds accumulated to pay the annual amount in perpetuity. Assume that the fund will earn an interest rate of i = 0.08 per annum. a. Determine the minimum number of deposits required to be made to accumulate to enough total funds to provide the annual scholarship amount in perpetuity. b. It has been decided that the required number of full $20! 000 payments will be made to establish the fund before commencing to pay the first scholarship. It is proposed that a second scholarship should be paid with an annual scholarship of $7,000, in perpetuity, but starting a number of years after the first scholarship commences. Find the earliest time that the second scholarship can commence if no additional funds are to be deposited and the accumulated funds are used to fund both scholarships. Problem 2 Consider a set of cash flows with present value given by (Ia)Toli + v10 (Dai a. Set out a cash flow diagram showing the amount and timing of cash flows corresponding to this present value and explain your answer. b. Prove that the following relationship holds: (Ia)10+ v0 (Da) = oli oli and explain clearly why this relationship holds using your cash flow diagram in a).

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Problem 1 a To determine the minimum number of deposits required to accumulate enough funds to provide the annual scholarship amount in perpetuity we need to calculate the present value of the perpetu... View the full answer