Basic Finance: Solving for (i) on a rate of return?

I've been trying to figure this one out for an hour now and the TI-83 doesn't even give me the correct answer, which is 15%. I need to understand how to solve it though.

An investment offers to pay you $10,000 a year for five years. If it costs $33,520, what will be your rate of return on the investment? Is $33,520 the present value??? I am so confused.

Yes, $33,520 is the present value of the investment and $10,000 are the annual rents. In your calculator if you enter the PV as a positive number you have to enter the rents as a negative number. N = 5, so the return is 15.002 percent per year.

If the return is 15%, then the PV is $33,521.55

Jim A is calculating the future value in his second calculation. I don't know what he is doing with the first calculation but it is wrong.

What do you mean by the cost? Is $33,520 your initial investment? If it is then I guess the total return over five years is 50,000 - 33,520 = 16,490 (~49%).
That's equivalent to 8.3% interest over 5 years.
(1.49 ^ (1/5)) ~= 1.083

A 15% return compounded 5 years on a 33,520 investment comes to $67,420 (1.15^5 * 33,520). I guess you're not getting all of that 15% back.

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/edit: Serge: I think I may have misunderstood the terminology and the question here. I also think see my mistake... If the interest was compounded in an account then it's equivalent to 8.3%. However the money is paid *out* of the account, so isn't accruing compound interest.

Therefore what you do is (working in thousands):
( 33.52 * 1.15 ) - 10 = 28.548 (first year)
( 28.548 * 1.15) - 10 = 22.830 (second year)
etc
comes to 0 after 5 years.

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What is more,
The formula for PV is PV = return / (1 + i)^n
the first year's PV is 10,000 / (1.15)
second year's PV is 10,000 / (1.15 * 1.15)
etc
add all the PVs together and you get 33,520
(this is basically the opposite of what I did just above).

Finding the interest rate from PV and the yearly returns would probably require an iterative process (i.e. use a calculator).