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Costco Executive Membership

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THE SCENARIO Earlier this week, I went shopping at Costco, where I get a lot of my staple foods, paper products, cleaning supplies, gasoline, and other essentials. I knew that my "Gold Star" membership was expiring, and that I would have to pay $60 to renew it in order to buy the things I wanted to buy that day. When I went up to the Membership counter, I saw that they also have an Executive membership, which costs $120. What do you get for that extra $60? The main thing is that at the end of the year, they send you a rebate check amounting to 2% of your purchases over the year. There are other advertised benefits, but I don't know that I'd be able to take advantage of any of them reliably, so I had to make my decision based entirely upon the rebate. So the question is this: If I want to make 15% on my money, how much would I need to spend per month (on average) to justify getting the Executive membership instead of just renewing my Gold Star membership?
THE SOLUTION This problem has 3 steps. First, I need to find out how big the end-of-year rebate check should be to make me 15% on the extra $60 that the executive membership costs. Then, I need to figure out how much I'd need to spend over the year to get a end-of-year rebate check of that amount. Then, I need to figure out how much I'd need to spend each month (on average) to add up to that total annual amount. Let's get started. Step 1 First things first, make sure the calculator is using 12 Payments per Year. N: 12 (I get the rebate check after one year) I/YR: 15 (I want to make 15% on my money) PV: -60 (I have to pay an extra $60 to get the Executive membership) PMT: 0 (I only get the rebate check at the end of the year; checks don't arrive in the meantime) FV: (this is what I'm trying to find)

The answer to Step 1 is that my rebate check would have to be at least $69.65 for me to make 15% on my money. Note that due to monthly compounding, this number is slightly higher than 115% of $60.

Step 2 2% of [total annual spending] = $69.65 2% is another way of writing 0.02 Therefore, [total annual spending] = $69.65 / 0.02 = $3,482.26

The answer to Step 2 is that I'd have to spend at least $3,482.26 over the next year to get a rebate check that large.

Step 3 If I spend $3,482.26 over a whole year, that means that I spend $3,482.26 / 12 each month (on average).

The answer to the whole question is that I'd have to spend an average of $290.19 per month in order to get a rebate check big enough to get me 15% on the extra $60 I'd spent on the Executive membership.

I generally don't spend $290.19 per month on staples at Costco, so upgrading to the Excecutive membership probably wouldn't make sense for me unless I thought it likely that I'd be buying one or more big-ticket items there (like a computer, iPad, TV, etc.) in the next year. In that case, I'd adjust the amount I'd need to spend in the year based on that extraordinary planned purchase (for example, if I planned to buy $2,500 worth of iPads, computers, TVs, and other big-ticket items, my annual number would go from $3,482.26 to $982.26) and use $982.26 to determine my required average monthly spending to compare with my normal monthly spending. Obviously, I wouldn't want to spend extra money just to get a 2% rebate, but if I'd already planned to do the spending, then setting up a rebate ahead of time might be a smart move. Does that make sense? Let us know what you think in the comments below!