Final answer:
A perpetuity with payments at the end of each four-year period, starting with a payment of 1 and increasing by 4 each time, has a present value of approximately 0.7874.
Step-by-step explanation:
A perpetuity is a type of financial investment that provides a continuous stream of cash flows with no designated end date. In this case, the perpetuity has payments at the end of each four-year period, starting with a payment of 1 at the end of the first four years.
Each subsequent payment is 4 more than the previous payment, so the second payment would be 5, the third payment would be 9, and so on.
The present value of a perpetuity is given by the formula PV = R / i, where PV is the present value, R is the payment amount, and i is the interest rate per period.
To solve for the present value of this perpetuity, we need to use the information given. We are told that v4 (which represents the present value at the end of four years) is 0.79.
Plugging in the values, we get 0.79 = 1 / i. Solving for i, we find that the interest rate per period is approximately 1.27.
Now, we can use this interest rate to find the value of the perpetuity. The first payment is 1, the second payment is 5, the third payment is 9, and so on. Adding up the present values of all the payments gives us the present value of the perpetuity.
To calculate the present value of the perpetuity, we can use the formula PV = R / i. Substituting the values, we get PV = 1 / 1.27 = 0.7874.
So, the present value of the perpetuity is approximately 0.7874.