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=2.96% p.a. effective and the first scholarship will be first awarded 2.5 years after the date of the donation. Assume that the fund's earnings rate rate has changed from j4=2.96% to j4=2.71% 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.93274.16
b.100410.89
c.97492.91
d.96377.03

Answer 1

In summary, to determine the additional amount to be added to the fund after an interest rate decrease, we would recalculate the fund's perpetuity value at the new rate and subtract the current fund's value from it. The scholarship amount is required for this calculation and is not provided in the question. Emma needs to make up the shortfall created by the interest rate decrease to maintain the scholarship amount.

Step-by-step explanation:

The question asks for the additional amount Emma needs to add to a fund to maintain the annual scholarship originally planned, given a changed interest rate one year before the first scholarship payment is due. This is a time-value of money problem that involves understanding compound interest and present value calculations. Since the interest rate is compounded quarterly (j4=2.71%), we first convert it to an effective annual interest rate.

To find the perpetuity value under the new interest rate of 2.71% compounded quarterly, we use the present value of a perpetuity formula PV = PMT / i, where PMT is the scholarship amount, and i is the annual effective interest rate. Assuming the scholarship amount (PMT) remains constant, we can calculate the difference between the new perpetuity value and the original million dollars to find out how much extra Emma needs to add.

Unfortunately, since critical numerical details like the scholarship amount (PMT) are missing, we cannot compute a specific numerical answer here. However, Emma would need to top up the fund with the difference between the original fund's value at the lower interest rate and the new perpetuity value required to maintain the annual scholarship at the desired amount.