Final Answer:
The present value of the perpetuity-immediate is $10,000.
Step-by-step explanation:
A perpetuity-immediate is a series of equal payments that continues indefinitely, and its present value can be calculated using the formula PV = PMT / i, where PV is the present value, PMT is the annual payment, and i is the interest rate. In this case, the annual payments are 1,000, 2,000, 3,000, 4,000, and so on, with an interest rate of 12%.
To find the present value, we use the formula PV = PMT / i. Plugging in the values, we get PV = 1,000 / 0.12 = $8,333.33 for the first payment, PV = 2,000 / 0.12 = $16,666.67 for the second payment, and so on. Adding up these present values for each annual payment results in a total present value of $10,000.
This means that if you were to receive these annual payments indefinitely and discount them back to their present value at a 12% annual rate, the total present value would be $10,000. The calculation takes into account the time value of money, reflecting the principle that a dollar received in the future is worth less than a dollar received today.