Question

Someone promises to pay you $1,000,000 every year (at the end of the year) for the next 15 years. The first payment will be one year from today. The relevant effective annual interest rate is 7.0%. What does the time line look like for this problem? What would you pay, today, for this promise?

For this we have to calculate the present value of the total cash inflow at interest rate of 7% for 15 years formula for this = cash inflow x P.V. annuity factor for 15 year @7%

Beginning	1 year	2 year	3 year	4 year	5 year	6 year	7 year
(00000)	$ 10	$ 10	$ 10	$ 10	$ 10	$ 10	$ 10

8 year	9 year	10 year	11 year	12 year	13 year	14 year	15 year
$ 10	$ 10	$ 10	$ 10	$ 10	$ 10	$ 10	$ 10

                                                                                               

Show that the answer in above example is the same as the difference between the present value of the following two perpetuities:

• Perpetuity 1 pays $1,000,000 at the end every year with the first payment made in 1year.
• Perpetuity 2 pays $1,000,000 at the end every year with the first payment made in 16years.

The relevant annual effective interest rate is 7.0%.

Answer 1

Explaination

As we know about the time value of money. A money kept today will lose its value in the near future and it become lower year by year. Therefore in the first alternative as we can see we have present value $ 9,107,914.01 however in the 2nd altenative present value remains $ 3,301,127.18. It is the clear indication that money loses its value with span of time.

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