Final answer:
To sustain quarterly perpetuity payments of $1000, the sum of money invested today is $18072.73 if the first payment is received three months from today, and $36363.64 if the first payment is received one year from today.
Step-by-step explanation:
To find the sum of money, invested today in a perpetual fund earning 5.5% compounded semiannually, that will sustain quarterly perpetuity payments of $1000, we can use the formula for the present value of a perpetuity.
a) For the first payment to be received three months from today, the interest rate will be compounded for one quarter. Therefore, the present value can be calculated as:
PV = Payment / (Interest Rate / Compounding Frequency) = $1000 / (0.055 / 4) = $18072.73
b) For the first payment to be received one year from today, the interest rate will be compounded for two quarters. Therefore, the present value can be calculated as:
PV = Payment / (Interest Rate / Compounding Frequency) = $1000 / (0.055 / 2) = $36363.64