For your twenty-first 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?

To determine which alternative you should choose, we need to calculate the future value of each option using compound interest.

Option 1: Receiving $1000 today.
Given that your money grows at a rate of 8 percent compounded annually, we can use the formula for compound interest:

Future Value = Present Value * (1 + Interest Rate)^Time

Time = 0 years
Present Value = $1000
Interest Rate = 8% or 0.08

Future Value = $1000 * (1 + 0.08)^0
Future Value = $1000

Option 2: Waiting 3 years and receiving $1500.
Time = 3 years
Present Value = $1500
Interest Rate = 8% or 0.08

Future Value = $1500 * (1 + 0.08)^3
Future Value = $1500 * (1.08)^3
Future Value = $1500 * 1.2597
Future Value ≈ $1,889.55

Option 3: Waiting 5 years and receiving $3000.
Time = 5 years
Present Value = $3000
Interest Rate = 8% or 0.08

Future Value = $3000 * (1 + 0.08)^5
Future Value = $3000 * (1.08)^5
Future Value = $3000 * 1.4693
Future Value ≈ $4,407.90

Now, we can compare the future values of each option.

Option 1: $1000
Option 2: $1,889.55
Option 3: $4,407.90

As you can see, waiting 5 years and receiving $3000 yields the highest future value. Therefore, waiting 5 years is the best alternative to choose if your money grows at a rate of 8 percent compounded annually.