Question

A village has five residents, each of whom has accumulated savings of $200. Each villager can use the money to buy a government bond that pays 10% interest per year or to buy a year-old goat, send it onto the commons to graze, and sell it after one year. The price of the goat that the villager will get at the end of the year depends on the amount of weight it gains while grazing on the commons, which in turn depends on the number of goats sent onto the commons, as shown in table below.

Number of goats on the commons Price per 2-year-old goat ($) Income per goat ($/year)
1 252 52
2 242 42
3 229 29
4 212 12
5 206 6

The villager will buy a year-old goat if it will command a price of at least _ as a 2-year old.

a) $240

b) $220

c) $210

d) $200

Answer 1

A villager will buy a year-old goat over a government bond if the goat will sell for at least $220 as a two-year-old, assuring an income that matches or exceeds the bond's interest.

Step-by-step explanation:

To determine whether it's more profitable to buy a government bond or to buy and sell a goat, compare the income from each option. A government bond that pays 10% interest on $200 will give $20 after one year. For buying and selling a goat to be more profitable, the end-of-year sale price of the goat, minus the initial $200 investment, must be greater than the $20 interest from the bond. To break even, the goat's price must be at least $220 ($200 investment + $20 bond interest).

According to the provided table, the goat price options are $252, $242, $229, $212, and $206 depending on the number of goats on the commons. Therefore, to command a price "at least as high" as the interest from the bond, the two-year-old goat needs to sell for a minimum of $220 to be considered.