Question

b)Everything else equal, which annuity has the greater future value: an     annuity or an annuity due? Why?

c) What is the difference between an ordinary annuity and an annuity due

d) All else equal, which annuity has the greater present value: an ordinary annuity or an annuity due? Why?

Answer 1

(b) Future Value of the annuity due is greater than the Future Value of the ordinary annuity.

Analysis of the above statement in point b)

With an annuity-due the payments are made at the beginning rather than the end of the period. The difference between the future value of an annuity due (AD) and future value of an ordinary annuity (OA) is based on the timing of the payments. ADs pay starting immediately, while OAs pay at the end of the period. Concept may be explained with the below mentioned example.

For example, let's say you are going to get an annuity that pays you $100 for 3 years. If that annuity is an AD, it will make the following payments:

1. $100 on 1/25/16

2. $100 on 1/25/17

3. $100 on 1/25/18

If that annuity is an OA, it will make the following payments:

1. $100 on 1/25/17

2. $100 on 1/25/18

3. $100 on 1/25/19

As you can see you'll receive $300 in total with either option. The only difference is that with the AD your payments will be completed 1 year sooner as they start on the day of the investment, whereas the OA starts 1 year following the day of the investment. The AD is more valuable than the OA due to the time value of money because you can invest that $100 you get today and get a return on it.

(c) Difference between an ordinary annuity and an annuity due

Key Differences Between Ordinary Annuity and Annuity Due

1. Ordinary annuity refers to the sequence of steady cash flow, whose payment is to be made or received at the end of each period. Annuity due implies the stream of payments or receipts which fall due at the beginning of each period.
2. Each cash inflow or outflow of an ordinary annuity is related to the period preceding its date. On the contrary, an annuity due, represent the cash flow period following its date. As the cash flows belonging to annuity due occur one period earlier than that of an ordinary annuity.
3. An ordinary annuity is best when an individual is making payment whereas annuity due is appropriate when a person is collecting payment. As the payment made on annuity due, have a higher present value than the regular annuity. This is because of the principle of time value of money, i.e. the value of one rupee, today is greater than the value of one rupee, after one year.
4. Payment of car loan, payment of mortgage and coupon bearing bonds are some examples of an ordinary annuity. On the flip side, the common examples of an annuity due are rental lease payments, car payments, payment of life insurance premium and so on.

(d) Present Value of the annuity due is greater than the Present Value of the ordinary annuity.

Analysis of the above statement in point d)

Why is the present value of the annuity due higher than that of the ordinary Because one more period of interest accrues - since payments are made at the beginning of each period instead of at the end of each period.