Question

You are offered $150 in exactly one year. Each year thereafter forever, you (or your estate) will receive an amount 2% higher than the previous year (so you will receive $153 in exactly two years, for example). From a purely present value perspective, would you prefer this infinite stream of payments or $10,000 cash today? Assume the interest rate is always 4%.a) Neitherb) The stream of payments starting in one yearc) $10,000 todayd) They are the same

Answer 1

Since , $10,000 is greater than the present value of $150 with 2% higher value each year (i.e $7500)

Hence,

the correct answer is option c) $10,000 today

Step-by-step explanation:

Given:

Amount offered in exactly 1 year = $150

Growth rate, g = 2% = 0.02

Interest rate, r = 4%

Now,

The present value of $150 =
`\frac{\textup{Amount Provided}}{(r-g)}`

on substituting the respective values, we get

The present value of $150 =
`(\$150)/((0.04-0.02))`

or

The present value of $150 = $7,500

Now,

The other offer provides an amount of $10,000 cash today

Since , $10,000 is greater than the present value of $150 with 2% higher value each year (i.e $7500)

Hence,

the correct answer is option c) $10,000 today