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solution

Suppose a person discounts future rewards hyperbolically according to the function PV(x) = x / (1 + k*t), where PV denotes the present value, x denotes the reward to be received, k is the discount rate per period of time and t is the delay until the reward is received. You offer this person the following deal: You ask the person today to promise to pay you $10 in 100 days in exchange for $14 in 101 days. After 100 days, you offer the person $10 on that day (100 days from now) in exchange for $15 the next day (101 days from now). For what range of discount rates (per day) will this deal make you money?

a) I can never make money

b) Less than 0.5

c) Greater than 0

d) Greater than 0.5

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