Question

A rich uncle gives you the choice of one of the following legacies:
a. $15,000 each year for the next 12 years
b. $13,000 each year for the next 18 years
c. $11,000 each year for the next 12 years plus a lump-sum payment of $81,000 at the end of the 18th year.
Which would you take and why? Assume that appropriate discount rate is 10 percent and all amounts would be received at the end of the year.

Answer 1

Answer on question #53341 – Economics/Finance

A rich uncle gives you the choice of one of the following legacies:

a. $15,000 each year for the next 12 years

b. $13,000 each year for the next 18 years

c. $11,000 each year for the next 12 years plus a lump-sum payment $81,000 at the end of the 18th year.

Which would you take and why?

Answer:

This formula was used for the calculations in all the variants:

$$\mathrm{FV} = \mathrm{PV} \times \left( \left( \frac{(1 + \mathrm{i})^n}{1} \right) \right) / \mathrm{i},$$

where FV – future value;

PV – present value;

n – period;

I – rate of percent

a. $\mathrm{FV} = \$15,000 \times \left( \frac{(1 + 0,10)^{12}}{1} \right) / 0,10 = \$320,764$

b. $\mathrm{FV} = \$13,000 \times \left( \frac{(1 + 0,10)^{18}}{1} \right) / 0,10 = \$592,789$

c. $\mathrm{FV} = \$11,000 \times \left( \frac{1 + 0,10}{12} \right) - \frac{1}{0,10} \cdot 81,000 \times \left( \frac{1 + 0,10}{18} \right)^{18} = \$235,227 + \$450,353 = \$685,580$

I made the choice ‘c’, because I can get more money among three variants.

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