Question

A perpetuity pays 1 at the end of the 1 st year, 2 at the end of the 2 nd year, 3 at the end of the 3 rd year, etc Which of the following expressions give the present value of this perpetuity? I.

i
2

1
​
II.
d
2

1−d
​
III. e
δ
+e
−δ
I and If only I and 111 only II and III only 1,11 and III

Answer 1

The present value of a perpetuity can be calculated using the formula: PV = R / i, where PV is the present value, R is the payment per period, and i is the interest rate per period. The correct expressions for the present value of the provided perpetuity are I, II, and III. The correct option is 4.

Step-by-step explanation:

The present value of a perpetuity can be calculated using the formula: PV = R / i, where PV is the present value, R is the payment per period, and i is the interest rate per period. In this case, the perpetuity pays 1 at the end of the first year, 2 at the end of the second year, 3 at the end of the third year, and so on. So the payment per period R is increasing by 1 each year. To calculate the present value, we need to find the sum of the present values of each payment.

Option I: i2 / (1+i) is incorrect because it assumes a constant interest rate, which is not the case here.

Option II: d2 / (1-d) is also incorrect because it assumes a constant discount rate, which is not the case here.

Option III: eδ + e-δ is incorrect because it is not related to the calculation of the present value of a perpetuity.

So the correct answer is option IV: I, II, and III.