Question

1) Assume the discount rate is given as r = 10% and consider an asset that makes the following year-end payments: $10 in year one, $20 in year two, and $30 in year three. Convert this asset into an equivalent three-year annuity.

a) What is the per-period payment of the annuity?

b) The fair price of an annuity is an increasing function of the underlying discount rate. True or False?

Answer 1

a)

The present value of all year end payments is calculated below:

This present value must be equal to present value of all future equivalent payments.

The per-period payment of annuity is calculated below:

b)

The discount rate declines with time. The given statement is false.