Question

A legal dispute delayed for 18 months the disbursement of a $500,000 bequest designated to provide quarterly payments in perpetuity to a hospice. While under the jurisdiction of the court, the funds earued interest at the rate of 5% compounded semianoually. The hospice has just invested the $500,000 along with its earuings in a perpetual fund earning 5.2% compounded semiannually. What payments will the hospice receive beginning three months from now?

Answer 1

To determine the quarterly payments, the compounded interest on $500,000 at a rate of 5% for 18 months must be calculated first, after which the new accumulated amount is invested at a 5.2% rate to provide perpetual quarterly payments.

Step-by-step explanation:

The student has asked how much the hospice will receive in quarterly payments from their investment, taking into account a legal delay and compound interest earnings. To solve this problem, we need to first calculate the total amount accumulated due to the compound interest over the 18 months delay at a 5% rate compounded semiannually. With this total amount, the hospice has then invested it into a perpetual fund at a 5.2% rate compounded semiannually, from which we need to determine the value of the quarterly payments.

To calculate the accumulated amount after 18 months (which is 3 semiannual periods) with a compound interest formula, we use:
A = P(1 + r/n)^(nt), where A represents the accumulated amount, P the principal amount ($500,000), r the annual interest rate (0.05), n the number of times the interest is compounded per year (2 for semiannual), and t the time in years (1.5 years). Then we apply the formula for perpetuity to find the quarterly payments: PMT = A * (r/n), where PMT is the payment per period, A is the accumulated amount, r is the annual interest rate (0.052), and n is the number of payments per year (4 for quarterly payments).