If you are offered $30,000 fifty years from now or $95 today, which would you choose and why?
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.
To determine whether you would choose $30,000 in 50 years or $95 today, you need to consider the concept of time value of money. The time value of money states that money available to you now is worth more than the same amount of money in the future. This is because of the potential to invest or earn interest on the money over time.
To evaluate the two options, you can use a financial concept called the present value. Present value is the current worth of an amount of money to be received in the future, accounting for the estimated rate of return or interest.
In this scenario, you need to consider how much the $30,000 would be worth in today's dollars, given a certain rate of return. Without knowing the rate of return, it is challenging to provide an exact answer. However, we can make a general comparison.
For simplicity, let's assume an annual rate of return of 5%. You can use a present value calculator or formula to calculate the present value of the $30,000 in 50 years. Using the present value formula, the calculation would look like this:
PV (Present Value) = FV (Future Value) / (1 + r)^n
PV = $30,000 / (1 + 0.05)^50 ≈ $2,052.41
The present value of $30,000 received in 50 years with a 5% annual rate of return would be approximately $2,052.41.
Comparing the present value of $2,052.41 to the immediate benefit of $95 today, it is evident that the $95 would offer more immediate value compared to the $30,000 received in 50 years. Therefore, based on this analysis, choosing the $95 today would be the preferred option.
However, do keep in mind that the actual decision depends on various factors, such as your investment opportunities, expected rate of return, inflation rates, and personal financial goals. It is important to consider these factors and adjust the analysis accordingly.