Question

A. Find the present value of the $50,000 twenty-year annuity. At 10%, the answer is $425,678.

b. Find the duration of this annuity. This is easiest using the closed-form equation.
c. Find a package of the bonds that has this duration and this market value.

Answer 1

a. $425678

Step-by-step explanation:

a. Pv = C[(1-(1+i)^-n)/i]

we will us the above mentioned formula for present value annuity as we are looking for the present value of the future payments of $50000 per year at 10% per annum.

given: C the periodic payment which is $50000 paid per annum

i the interest rate per period which is 10% per annum

n is the periods that the amount is paid for which is 20 years in this case.

therefore Pv = 50000[(1-(1+10%)^-20)/10%] then we compute and get

Pv = $425678.19

wich is $425678 rounded off to the nearest dollar.

Answer 2

a. $425,678.

b. 20 years

c. net present value, bond yields, spot rates, and pension obligations.

Step-by-step explanation:

a.

In order to find the present value we have to apply in the following formula

`P = PMT * (1-(1)/((1+r)^(n) ) )/(r)`

where

P = Present value of an annuity stream

PMT = Dollar amount of each annuity payment

r = Interest rate (also known as discount rate)

n = Number of periods in which payments will be made

Replacing values we have that

`P = 50000 * (1-(1)/((1+0.1)^(20) ) )/(0.1)`

P = $425,678

b.

As written in the exercise, 20 years for a present value of $425,678

c.

The package of bonds can include net present value, bond yields, spot rates, and pension obligations.