Emma wants to donate $1,000,000 to establish a fund to provide an annual scholarship in perpetuity. The fund will earn an interest rate of j4=4.12% p.a. effective and the first scholarship will be first awarded 2.5 years after the date of the donation. (a) What is the amount of the annual scholarship (rounded to two decimal places)? (b) Assume that the fund's earnings rate rate has changed from j4=4.12% to j4=3.87% one year before the first scholarship payment. How much does Emma need to add to the fund at that time (one year before the first scholarship payment) to ensure that scholarship amount will be unchanged (rounded to two decimal places)?

(a) What is the amount of the annual scholarship (rounded to two decimal places)?

a.

44494.20

b.

46355.87

c.

41840.92

d.

43772.21

(b) Assume that the fund's earnings rate rate has changed from j₄=4.12% to j₄=3.87% one year before the first scholarship payment. How much does Emma need to add to the fund at that time (one year before the first scholarship payment) to ensure that scholarship amount will be unchanged (rounded to two decimal places)?

a.

68632.57

b.

69756.01

c.

72674.67

d.

65596.33