I had these questions for homework, I have already worked them but I don't understand how my answer is wrong.

Exhibit 8-1
The cash flows associated with an investment project are as follows:
Cash Flows
Initial Outflow -$70,000
Year 1 $20,000
Year 2 $30,000
Year 3 $30,000
Year 4 $30,000

NARREND
Refer to Exhibit 8-1. What's the payback period of the project? If a firm's cutoff payback period is 3 years, should it accept the project?

When I worked it I got 2.7 years for the project & you would accept it, however my answer appendix is saying that the correct answer is 3.6 years accept the project.

I worked it by using the first full 2 years which gives you 50,000 then you only need 20,000 out of the 30,000 from year 3 so when you divide 20,000/30,000 then you get .667 and add that to the full 2 years to get 2.7 years. If you could just please tell me where I made a mistake.

I think your answer is correct and the book is wrong.

you are correct and the book answer is incorrect. The only reason I would say they have 3.5 years is probably they used a discount rate and discounted the cash flows for each year to the present. The author might have accidentally tried to do it that way forgetting the problem is asking for Payback and not net present value

One hint that the book is wrong is that the it's answer exceeds the 3 year payback cutoff period and yet it wants to accept the project.