For your 21st birthday, your grandfather offers you a gift of $1000 today.
However, you have the choice of waiting 3 years and receiving $1500 OR waiting 5 years and receiving $3000.
If your money grows at a rate of 8 percent compounded annually, which alternative should you choose?
Thank you for your help!
Well, I must say, that's a tough decision. It's like trying to choose between cake and ice cream – they're both delicious, but you can only have one.
Now let's do some clown math here. If you take the $1000 now and invest it at an 8% interest rate, compounded annually, after 3 years you would have $1000 * (1 + 0.08)^3 = $1259.71.
On the other hand, if you wait 3 years and receive $1500, you don't need any math skills because it's a no-brainer.
But wait, there's more! If you decide to wait another 2 years (for a total of 5 years), and receive $3000, the calculation is a bit trickier. After 5 years, your initial $1000 would have grown to $1000 * (1 + 0.08)^5 = $1469.33.
So, if we compare the two options, it seems that waiting for 5 years and receiving $3000 would give you more money in the end. But hey, who doesn't love instant gratification?
Ultimately, the choice is up to you, my friend. Take your pick and enjoy the bounty!
To determine which alternative you should choose, we can calculate the future values of the options and compare them.
First, let's calculate the future value if you take the $1000 gift and invest it at an 8% annual interest rate compounded annually for 3 years:
Future Value (Option 1) = $1000 * (1 + 0.08)^3
Future Value (Option 1) = $1000 * (1.08)^3
Future Value (Option 1) = $1000 * 1.2597
Future Value (Option 1) = $1259.70
Next, let's calculate the future value if you wait 3 years and receive $1500:
Future Value (Option 2) = $1500
Finally, let's calculate the future value if you wait 5 years and receive $3000:
Future Value (Option 3) = $3000
Comparing the future values of the options, we can see that:
Future Value (Option 1) = $1259.70
Future Value (Option 2) = $1500
Future Value (Option 3) = $3000
Since the future value of Option 3 ($3000) is the highest, waiting 5 years and receiving $3000 is the better choice compared to taking the $1000 gift or waiting 3 years to receive $1500.
To determine which option is better, let's calculate the value of each alternative using the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years
Let's calculate the value of each alternative:
Alternative 1:
P = $1000
r = 8% = 0.08
n = 1 (compounded annually)
t = 3 years
A1 = 1000(1 + 0.08/1)^(1*3)
A1 = 1000(1.08)^3
A1 = 1000 * 1.2597
A1 ≈ $1259.70
Alternative 2:
P = $1000
r = 8% = 0.08
n = 1 (compounded annually)
t = 5 years
A2 = 1000(1 + 0.08/1)^(1*5)
A2 = 1000(1.08)^5
A2 = 1000 * 1.4693
A2 ≈ $1469.30
Based on these calculations, if you choose to wait three years to receive $1500, the value of your money will be approximately $1259.70. On the other hand, if you choose to wait five years to receive $3000, the value of your money will be approximately $1469.30.
Therefore, the better alternative in terms of maximizing the value of your money is to wait five years and receive $3000.
To determine what you would have at the end of 3 or 5 years use:
The following formula works for compounded annually.
future value = P(1+r)^n
for 1500 and 3 years at 8%
1500(1+.08)^3
Do this calculation and a similar one for the 5 year period and then compare.