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 can earn 10 percent annually, which alternative would you choose? If you could earn 11 percent annually, would you still choose the same alternative? Please explain your answer in at least 7-8 well-developed sentences.

The present value at 10% is computed as shown below:

The present value of alternative 1 will be $ 7,500 since the same is received now i.e. today

The present value of alternative 2 is computed as follows:

Present value = Annual amount x [ (1 – 1 / (1 + r)ⁿ) / r ]

= $ 2,200 x [ (1 - 1 / (1 + 0.10)⁹ ) / 0.10 ]

= $ 2,200 x 5.759023816

= $ 12,669.85 Approximately

The present value of alternative 3 is computed as follows:

= Future value / (1 + interest rate)^{time period}

= $ 31,000 / 1.10⁹

= $ 31,000 / 2.357947691

= $ 13,147.03

Since the present value of Alternative 3 is the greatest amongst the 3 alternatives, hence Alternative 3 shall be selected.

The present value at 11% is computed as shown below:

The present value of alternative 1 will be $ 7,500 since the same is received now i.e. today

The present value of alternative 2 is computed as follows:

Present value = Annual amount x [ (1 – 1 / (1 + r)ⁿ) / r ]

= $ 2,200 x [ (1 - 1 / (1 + 0.11)⁹ ) / 0.11 ]

= $ 2,200 x 5.537047532

= $ 12,181.50 Approximately

The present value of alternative 3 is computed as follows:

= Future value / (1 + interest rate)^{time period}

= $ 31,000 / 1.11⁹

= $ 31,000 / 2.558036924

= $ 12,118.67

Since the present value of Alternative 2 is the greatest amongst the 3 alternatives, hence Alternative 2 shall be selected.

We shall not choose the same alternative, since as we increased the interest rate, the present value of Alternative 3 has reduced and is less than the present value of Alternative 2.

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