Question

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

Answer:

C  $ 14.550

TRUE

A higher discount rate would make the annuities present value increase.

While a lower discount rate makes the present value (fair value today) decrease

Explanation:

First, we calcualte the PV

Then, we solve fo the annuity whihc generates the same PV

$\frac{cash \: flow}{(1 + rate)^{time} } = PV$  

discount rate: 10%  = 10/100 =  0.1

1   10.00    9.09

2   20.00   16.53

3   30.00   22.54

 Total    48.16

$PV \div \frac{1-(1+r)^{-time} }{rate} = C$

PV 48.16

time 3 years

rate 0.10

$48.16 \div \frac{1-(1+0.1)^{-3} }{0.1} = C$

C  $ 14.550