Question

You are offered an annuity investment that will pay you $ 25,000 per year for 10 years     beginning in 20 years. These payments will be made at the beginning of each year and your discount rate is expected to be 8%. You will need to make payments at the end of each year for the next 20 years (also at 8%) in order to receive the annuity investment.

What is the present value of the annuity investment as of 20 years from now?
How much payments you will need to make for the next 20 years to get the annuity?

Answer 1

Solution:

Given:

Annuity received = $25,000 at the beginning of the year

Duration = 10 years

Discount rate = 8%

First Receipt = At the beginning of 21^st year i.e., at teh end of 20^th year

a. Calculation of Value of Total receipt as at the end of 20^th year:

b. Calculation of Present Value of the Annuity Investments as of 20 years from now:

According to question:

Future value of annuity made for 20 years with the return of 20% = Value of Annuities received at the beginning of year for 10 years from 21 year.

Therefore, Present Value of Annuity Investments as of 20 years from now =

= 0.214548 * 181172.197771

=38870.17

c. Calculation of Payment for next 20 years to get the annuity:

As payments are made at the end of year:

Present Value Annuity factor =

= 9.818147

Annuity =

=

=3959.012699

So, we need to pay annually $ 3,959.01 for 20 years to get receive an annuity of $25,000 from the beginning of 21^st year.

Cross Check for receipt of annuity:

Cross Check for Payment: