Question #58578

Your grandfather has offered you a choice of one of the three following alternatives: $7,500 now; $2,200
a year for nine years; or $31,000 at the end of nine years. Assuming you could earn 10 percent annually,
which alternative should you choose? If you could earn 11 percent annually, would you still choose the
same alternative?

Expert's answer

to define the best alternative of the offered choices we need to compare them on the same basis, that is, NPV (net present value calculated using the same interest rate).

For the interest rate of 10% the options are as follows:

1. NPV $7,500 = $7,500

2. NPV of annuity of $2,000 during 9 years = $12,670

3. NPV of $31,000 at the end of the 9th year = $13,147

So the third option is the optimal choice.

For the interest rate of 11% the options are as follows:

1. NPV $7,500 = $7,500

2. NPV of annuity of $2,000 during 9 years = $12,182

3. NPV of $31,000 at the end of the 9th year = $12,119

Now the best choice is the second option.

For the interest rate of 10% the options are as follows:

1. NPV $7,500 = $7,500

2. NPV of annuity of $2,000 during 9 years = $12,670

3. NPV of $31,000 at the end of the 9th year = $13,147

So the third option is the optimal choice.

For the interest rate of 11% the options are as follows:

1. NPV $7,500 = $7,500

2. NPV of annuity of $2,000 during 9 years = $12,182

3. NPV of $31,000 at the end of the 9th year = $12,119

Now the best choice is the second option.

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