Question

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)?
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

Answer 1

The amount of the annual scholarship is $24,271,844.66. Emma needs to add $25,193,750.96 to the fund one year before the first scholarship payment to ensure the scholarship amount remains unchanged.

Step-by-step explanation:

(a) To calculate the amount of the annual scholarship, we can use the formula for the present value of a perpetuity:

Present Value (PV) = Annual Scholarship Amount / Interest Rate

Plugging in the given values, we have:

PV = 1,000,000 / 0.0412 = $24,271,844.66

Rounded to two decimal places, the amount of the annual scholarship is $24,271,844.66.

(b) To calculate how much Emma needs to add to the fund one year before the first scholarship payment to ensure that the scholarship amount remains unchanged, we can use the formula for the future value of a lump sum:

Future Value (FV) = Principal + (Principal x Interest Rate)

Plugging in the given values, we have:

FV = 24,271,844.66 + (24,271,844.66 x 0.0387) = $25,193,750.96

Rounded to two decimal places, Emma needs to add $25,193,750.96 to the fund one year before the first scholarship payment.