Question

Mr. Chan has donated $1 million to a college to set up a perpetuity for the purchase of books and journals for a new library to be built and named in his honour. The donation will be invested and earnings will compound for three years, at which time the first of the quarterly perpetuity payments will be made. If the funds earn 6% compounded quarterly, what will be the size of the payments?

Answer 1

The size of the perpetuity payments will be approximately $836,290.77.

Step-by-step explanation:

The student is asking about the calculation of quarterly payments from an investment that has been given time to grow through compound interest. In this scenario, Mr. Chan has donated $1 million, which will be invested at a rate of 6% compounded quarterly for three years before beginning quarterly perpetuity payments. The size of these quarterly payments can be determined using the formula for the present value of a perpetuity. To calculate the size of the perpetuity payments, we need to use the formula:

Payment = Principal / ((1 + r)^n)

Where:
Principal = $1,000,000
r = yearly interest rate / number of compounding periods per year = 6% / 4 = 1.5%
n = number of compounding periods = 3 years * 4 quarters = 12 quarters

Using these values, we can calculate the size of the perpetuity payments:

Payment = $1,000,000 / ((1 + 1.5%)^12)

Payment ≈ $1,000,000 / (1.015^12)

Payment ≈ $1,000,000 / 1.195618

Payment ≈ $836,290.77