Final answer:
Jack inherited a perpetuity with annual payments of $10,000. He exchanged the first 10 payments for a perpetuity with the same present value. The annual payment for both perpetuities is $10,000.
Step-by-step explanation:
Jack inherited a perpetuity-due with annual payments of $10,000. A perpetuity is a series of equal payments that continue indefinitely. In this case, the perpetuity has payments due at the beginning of each period.
To find the present value of the perpetuity-due, we can use the formula:
PV = PMT / r
Where PV is the present value, PMT is the annual payment, and r is the discount rate. Since the payments are at the beginning of each period, we use the 'annuity-due' formula which discounts the payments by one period.
However, the question states that Jack exchanged the first 10 payments for a perpetuity-immediate with the same present value. A perpetuity-immediate has payments due at the end of each period. The present value formula for a perpetuity-immediate is:
PV = PMT / r
Since both perpetuities have the same present value, we can equate the formulas and solve for PMT:
PMTdue / r = PMTimmediate / r
PMTdue = PMTimmediate
Therefore, the annual payment of the perpetuity-due is equal to the annual payment of the perpetuity-immediate, which is $10,000.