Question

Jones purchased a perpetuity today for $7000. What is the value of the perpetuity if the interest rate is 5%?

Answer 1

A perpetuity is a financial instrument that promises a fixed sum of money to be paid indefinitely at regular intervals. To calculate the value of a perpetuity, you can use the formula: PV = C / r, where PV is the present value, C is the cash flow, and r is the interest rate.

Step-by-step explanation:

A perpetuity is a financial instrument that promises a fixed sum of money to be paid indefinitely at regular intervals. To calculate the value of a perpetuity, you can use the formula:

PV = C / r

Where PV is the present value, C is the cash flow (in this case $7000), and r is the interest rate (in this case 5%).

Plugging in the values, we get:

PV = 7000 / 0.05 = $140,000

Therefore, the value of the perpetuity is $140,000.

Answer 2

Using the perpetuity formula, the annual payment for the perpetuity purchased by Jones is $350 indefinitely, with the value of the perpetuity remaining at $7000 at a 5% interest rate.

Step-by-step explanation:

Jones purchased a perpetuity today for $7000. The value of a perpetuity is calculated using the formula Perpetuity Value = Payment / Interest Rate. In order to find the payment being made by the perpetuity, we rearrange the formula to Payment = Perpetuity Value × Interest Rate. Assuming a 5% interest rate, we apply the values into the formula: Payment = $7000 × 0.05, which equals $350 per year indefinitely.

In other words, the $7000 is the present value of a perpetual series of annual payments of $350, if the discount rate (or interest rate) is 5%. Therefore, the value of the perpetuity remains $7000, as long as the interest rate does not change.