Problem: \"Suppose you discount the future at a rate of 10% per year. in other w

Question

Problem: "Suppose you discount the future at a rate of 10% per year. in other words, a dollar a year from now has a present value of 90 cents. A dollar two years from now has a present value of 81 cents. (a) This is not quite equivalent to an interest raet of 10%. What interest rate (to within .01%, calculator will be needed) corresponds to this sort of discounting of the future? (b) Next, suppose somebody offers to sell you a tree that sheds 5 dollars each year. The first "payment" of 5 dollars is right now, and the second payment is one year from now, and so on; forever! How much would you be willing to pay for this tree?"

Answers: (a) is easy, it's 11.11%.

for (b) I think the infinite sum formula for perpetuities is principal*1/r, so in this case it would be 5*1/.1 which is just $50. However, it says the first payment is right now, when usually payments start after the first period or year. Does this change the answer?

Explanation / Answer

PV = 5 + 5/(1.1) + 5/1.1^2 + 5/1.1^3 +........Infinity

and you know

5/(1.1) + 5/1.1^2 + 5/1.1^3 +........Infinity = 5/0.1 = $ 50

so PV = 5 + 50 = $55

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