Posted by TinkRose on Thursday, January 14, 2010 at 2:05pm.
A bird in the hand is worth two in the bush. I'd take $95 today. The chances are slim that anyone over 30 now will be alive and able to enjoy $30,000 in fifty years.
What Ms. Sue wrote is not the case. You need the interest rate to continue on in the problem.
You can not compare sums of money in different time periods. So, we have to discount the $30,000 to be in terms of today's dollars. $30,000 in fifty years is not worth $30,000 today. We would need to solve:
PV = 30,000/(1+r)^50
To get the present value of the $50,000 in today's dollars, given the prevailing interest rate (and assuming that rates will be constant over that 50 years, which I'm assuming you are doing).
If we take an example rate of 10%, we can plug in and solve:
PV = 30,000/(1.10)^50 = $255.56
Which is greater than the $95 you are receiving today. To find out which rate would make you indifferent between the two outcomes, you would solve:
30,000/(1 + r)^50 = 95
Where r is the rate written as a decimal (ex: 3% = 0.03)
If D0 = $2.00, g (which is constant) = 6%, and P0 = $40, what is the stock’s expected dividend yield for the coming year? a. 5.0% b. 5.1% c. 5.3% d. 5.6% e. 5.8%
A share of common stock has just paid a dividend of $2.00. If the expected long-run growth rate for this stock is 7%, and if investors require a(n) 11% rate of return, what is the price of the stock?
PV = FV/(1+i)^n FV n "Compounding
Periods" n i i FVIF PV
$30,000.00 50 1 50 12% 0.12 $289.002 $103.81
Present Value of $30,000 today is $103.80 when compared to $95 that he is getting today, therefore the kid should take $30,000 in 50 years.