You want to endow a scholarship that will pay $10,000 per year forever, starting one year from now. if the school’s endowment discount rate is 7%, what amount must you donate to endow the scholarship? 13. how would your answer to problem 12 change if you endow it now, but it makes the first award to a student 10 years from today?

12. $142,857.14

13. $77,704.82 . . . it is changed by the accumulated interest on the amount

Step-by-step explanation:

12. You want one year's interest on the endowment to be equal to $10,000. The principal (P) can be found by ...

  I = Prt

  10,000 = P·0.07·1

  10,000/0.07 = P ≈ 142,857.14

The endowment must be $142,857.14 to pay $10,000 in interest annually forever.

__

13. If the first award is in 10 years, we want the above amount to be the value of an account that has paid 7% interest compounded annually for 9 years. (The first award is 1 year after this amount is achieved.) Then we want the principal (P) to be ...

  142,857.14 = P·(1 +0.07)^9

  142,57.14/1.07^9 = P = 77,704.82

The endowment needs to be only $77,704.82 if the first award is made 10 years after the endowment date.

x = -3

y = -18

step-by-step explanation:

to solve by substitution, substitute one variable and solve for the other. then substitute again to find the remaining variable.

x-1/3(3x-9) = -3 since y=3x-9 substittute y.

x-1/3(3x-9)=-3

x + x +3 = -3

2x+3=-3

2x+3-3= -3-3

2x=-6

x=-3

substitute again into y=3x-9

y=3(-3)-9

y=-9-9

y=-18